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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,341 papers · 148 categories

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48 results for “pseudo-euclidean space”

Classification of conformal solitons in pseudo-Euclidean spacesmath.DG

The paper classifies conformal solitons in pseudo-Euclidean spaces.

problem Classifying conformal solitons in pseudo-Euclidean spaces.

method Classification through pseudo-Riemannian hypersurfaces and position vector fields.

result Complete classification of conformal solitons in pseudo-Euclidean spaces.

conformal solitons pseudo-Riemannian hypersurfaces pseudo-Euclidean spaces Yamabe solitons

2022-01-14abs ↗pdf ↗

ε

-isothermic surfaces in pseudo-Euclidean 3-spacemath.GT

The paper studies special surfaces in pseudo-Euclidean space.

problem Characterizing and classifying

ε

-isothermic surfaces in pseudo-Euclidean 3-space.

method Analyzing the pseudo-Calapso equation and providing explicit coordinates for Dupin surfaces.

result Explicit solutions to the pseudo-Calapso equation are provided.

pseudo-Euclidean space isothermic surfaces Dupin surfaces pseudo-Calapso equation

2020-12-07abs ↗pdf ↗

Medial Axis in Pseudo-Euclidean Spacesmath.DG

Examines medial axis in pseudo-Euclidean spaces.

problem No specific problem stated; focuses on new context.

method Follows Birbrair and Denkowski's approach.

result Feasibility of medial axis in pseudo-Euclidean spaces checked.

Medial Axis Pseudo-Euclidean Spaces Birbrair Denkowski

2025-02-10abs ↗pdf ↗

Warped product hypersurfaces in the pseudo-Euclidean spacemath.DG

Study on hypersurfaces in pseudo-Euclidean space with constant curvature or rotational properties.

problem Characterizing hypersurfaces in pseudo-Euclidean space.

method Defined and studied warped product hypersurfaces with constant sectional curvature or rotational properties.

result Hypersurfaces in pseudo-Euclidean space either have constant curvature or are contained in rotational hypersurfaces.

Hypersurfaces Pseudo-Euclidean space Warped product Constant curvature Rotational hypersurfaces

2022-08-16abs ↗pdf ↗

On the classification of ruled minimal surfaces in pseudo-Euclidean spacemath.DG

The paper classifies ruled minimal surfaces in pseudo-Euclidean space.

problem Classifying ruled minimal surfaces in pseudo-Euclidean space.

method Complete classification in generic situations, discussing existence conditions.

result Complete classification of ruled minimal surfaces in pseudo-Euclidean space.

ruled surfaces minimal surfaces pseudo-Euclidean space classification

2017-05-09abs ↗pdf ↗

Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo Euclidean Space E4-2math.DG

Study on special surfaces in 4D pseudo-Euclidean space with specific Gauss maps.

problem Characterizing rotational surfaces with pointwise 1-type Gauss maps in E4-2.

method Analyzing surfaces with spacelike profile curves in E4-2.

result Characterizations for surfaces to have pointwise 1-type Gauss maps.

pseudo-Euclidean space rotational surfaces Gauss map spacelike profile curve

2016-01-19abs ↗pdf ↗

Notes on Degenerate Curves in Pseudo-Euclidean Spaces of Index Twomath.DG

In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the $6-$ dimensional pseudo-Euclidean space of index two. Also we characte…

2011-06-17abs ↗pdf ↗

Rigidity theorems of spacelike entire self-shrinking graphs in the pseudo-Euclidean spacemath.DG

The paper proves rigidity for self-shrinking spacelike graphs in pseudo-Euclidean space.

problem Understanding the rigidity of self-shrinking spacelike graphs in pseudo-Euclidean space.

method Volume growth estimate and Co-Area formula.

result Various rigidity results for spacelike entire self-shrinking graphs.

rigidity spacelike self-shrinking graphs pseudo-Euclidean

2019-10-17abs ↗pdf ↗

Rotational Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-Space with Neutral Metricmath.DG

Classifies surfaces with constant mean curvature in a specific type of space.

problem Classifying surfaces with constant mean curvature in a specific type of space.

method Classification based on the type of curvature (elliptic, hyperbolic, parabolic) and the rotational nature of the surfaces.

result Classification of constant mean curvature rotational surfaces.

constant mean curvature rotational surfaces pseudo-Euclidean space neutral metric

2016-01-20abs ↗pdf ↗

Parametrizations of minimal timelike surfaces in the four-dimensional pseudo-Euclidean space of index twomath.DG

New parametrizations for minimal timelike surfaces discovered.

problem Finding parametrizations for minimal timelike surfaces in specific spaces.

method Derived representation formulas for null curves leading to parametrizations of minimal timelike surfaces.

result Examples of minimal timelike surfaces constructed.

minimal timelike surfaces pseudo-Euclidean space null curves representation formulas

2026-02-21abs ↗pdf ↗

Spacelike Brakke flows with boundary in pseudo-Euclidean spacemath.DG

Develops weak formulation for spacelike flows in pseudo-Euclidean space.

problem Weak formulation of spacelike mean curvature flow in pseudo-Euclidean space.

method Based on spacelike integer rectifiable varifolds and pseudo-Euclidean first variation.

result Existence and compactness of spacelike Brakke flows with fixed boundary.

pseudo-Euclidean space spacelike flows mean curvature flow varifolds compactness

2026-07-11abs ↗pdf ↗

Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-space with Neutral Metricmath.DG

The study classifies meridian surfaces with constant mean curvature in a special pseudo-Euclidean space.

problem Classifying meridian surfaces with constant mean curvature in a pseudo-Euclidean space.

method Analyzing one-parameter systems of meridians of rotational hypersurfaces in a four-dimensional pseudo-Euclidean space with neutral metric.

result Complete classification of meridian surfaces with constant mean curvature, including minimal and quasi-minimal surfaces.

Meridian surfaces Constant mean curvature Pseudo-Euclidean space Rotational hypersurfaces Neutral metric

2016-05-31abs ↗pdf ↗

The Light ray transform for pseudo-Euclidean metricsmath.DG

Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.

problem Analyzing light ray transform in pseudo-Euclidean space.

method Investigate normal operator, derive inversion formula, analyze as Fourier Integral Operator.

result Derive an inversion formula and prove stability estimates.

ray transform pseudo-Euclidean space light rays Fourier Integral Operator stability estimates

2025-02-19abs ↗pdf ↗

Congruence of hypersurfaces of a pseudo-Euclidean spacemath.DG

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

2010-08-30abs ↗pdf ↗

General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metricmath.DG

Study on surfaces in pseudo-Euclidean space with neutral metric.

problem Characterizing surfaces in pseudo-Euclidean 4-space with neutral metrics.

method Defined and studied Lorentz general rotational surfaces with specific properties.

result Complete classification of various types of general rotational surfaces.

pseudo-Euclidean space neutral metric general rotational surfaces Lorentz surfaces minimal surfaces

2016-07-14abs ↗pdf ↗

On rotational surfaces with zero mean curvature in the pseudo-Euclidean space

\mathbb{E}_2^4

math.DG

Study of surfaces with zero mean curvature in a specific pseudo-Euclidean space.

problem Characterizing surfaces with zero mean curvature in a pseudo-Euclidean space.

method Solving differential equations to determine profile curves and explicit parametrizations.

result Explicit parametrizations of maximal and timelike surfaces with zero mean curvature.

pseudo-Euclidean space rotational surfaces zero mean curvature differential equations profile curves

2016-07-26abs ↗pdf ↗

The Duality principle for Osserman algebraic curvature tensorsmath.DG

The duality principle connects algebraic curvature tensors in pseudo-Euclidean spaces.

problem Understanding algebraic curvature tensors in pseudo-Euclidean spaces.

method Proving equivalence between the Jordan-Osserman condition and the Rakić duality principle.

result The Osserman condition and the duality principle are equivalent in the diagonalisable case.

algebraic curvature tensors pseudo-Euclidean spaces Jordan-Osserman condition Rakić duality principle Osserman condition

2015-12-22abs ↗pdf ↗

Exact algebraic M(em)brane solutionsmath.DG

New, algebraic surfaces found in curved spaces.

problem Finding new types of surfaces in curved spaces.

method Analyzing zero-mean-curvature hypersurfaces in pseudo-Euclidean spaces.

result Three new classes of algebraic surfaces discovered.

algebraic surfaces zero-mean-curvature pseudo-Euclidean spaces

2021-06-28abs ↗pdf ↗

Lagrangian mean curvature flow in Pseudo-Euclidean spacemath.AP

We establish the longtime existence and convergence results of the mean curvature flow of entire Lagrangian graphs in Pseudo-Euclidean space which is related to Logarithmic gradient flow.

2009-08-21abs ↗pdf ↗

A Classification of Biconservative Hypersurfaces in a Pseudo-Euclidean Spacemath.DG

The paper classifies biconservative hypersurfaces in a 5D pseudo-Euclidean space.

problem Classifying biconservative hypersurfaces in a pseudo-Euclidean space.

method Analyzing hypersurfaces with specific curvature properties and shape operators.

result Complete classification of biconservative hypersurfaces with certain curvature conditions.

biconservative hypersurfaces pseudo-Euclidean classification curvature

2015-12-20abs ↗pdf ↗

The Clairaut's theorem on rotational surfaces in pseudo Euclidean 4-space with index 2math.DG

The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.

problem Exploring geodesic curves on rotational surfaces in pseudo-Euclidean 4-space.

method Expressing Clairaut's theorem and deriving equations for geodesic curves.

result Characterization of geodesic curves on hyperbolic and elliptic surfaces of rotation.

Clairaut's theorem pseudo-Euclidean 4-space geodesic curves rotational surfaces

2021-07-31abs ↗pdf ↗

Quasi-minimal Lorentz Surfaces with Pointwise 1-type Gauss Map in Pseudo-Euclidean 4-Spacemath.DG

The study classifies quasi-minimal Lorentz surfaces with specific Gauss maps.

problem Classifying quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.

method Analyzing Lorentz surfaces in a four-dimensional pseudo-Euclidean space with neutral metric.

result Complete classification of quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.

Lorentz surfaces pseudo-Euclidean space quasi-minimal pointwise 1-type Gauss map mean curvature vector

2015-11-18abs ↗pdf ↗

Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metricmath.DG

Minimal Lorentz surfaces in pseudo-Euclidean 4-space are characterized by specific curvature conditions.

problem Characterizing minimal Lorentz surfaces in a specific geometric space.

method Introducing canonical parameters and solving a system of partial differential equations.

result Minimal Lorentz surfaces of general type are uniquely determined by two invariant functions.

Minimal surfaces Lorentz geometry Pseudo-Euclidean space Curvature conditions Partial differential equations

2017-05-17abs ↗pdf ↗

Invariant solutions of gradient

k

-Yamabe solitonsmath.DG

The paper classifies invariant gradient $k$ -Yamabe solitons in pseudo-Euclidean spaces.

problem Characterizing invariant gradient

k

-Yamabe solitons in pseudo-Euclidean spaces.

method Characterization through the action of an

(n-1)

-dimensional translation group and classification of rotational invariant solutions.

result Infinitely many explicit examples of geodesically complete steady gradient

k

-Yamabe solitons are constructed.

Yamabe solitons pseudo-Euclidean spaces translation group steady solitons geodesic completeness

2021-08-10abs ↗pdf ↗

Frobenius Manifolds as a Special Class of Submanifolds in Pseudo-Euclidean Spacesmath.DG

We introduce a class of potential submanifolds in pseudo-Euclidean spaces (each N-dimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanif…

2007-10-31abs ↗pdf ↗

Pseudo-Riemannian geodesics and billiardsmath.DG

Many classical facts in Riemannian geometry have their pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure.…

2006-08-24abs ↗pdf ↗

Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spacesmath.DG

We introduce a class of k-potential submanifolds in pseudo-Euclidean spaces and prove that for an arbitrary positive integer k and an arbitrary nonnegative integer p, each N-dimensional Frobenius manifold can always be locally realized as an N-dimensional k-potential submanifold in ((k + 1) N + p)-dimensional pseudo-Eu…

2009-11-22abs ↗pdf ↗

Reduction of gradient Ricci soliton equationsmath.DG

Reduces gradient Ricci solitons to ODEs for easier analysis.

problem Solving complex gradient Ricci soliton equations.

method Conformal reduction to ODEs for easier analysis.

result Gradient Ricci solitons are invariant under specific groups.

gradient Ricci solitons partial differential equations ordinary differential equations pseudo-Euclidean space reduction

2018-05-10abs ↗pdf ↗

Static Einstein-Maxwell space-time invariant by translationgr-qc

Study static Einstein-Maxwell space invariant by translation.

problem Classify static Einstein-Maxwell space invariant under translation.

method Analyze static Einstein-Maxwell space conformal to pseudo-Euclidean space.

result Complete classification of static Einstein-Maxwell space invariant under translation.

Einstein-Maxwell space static space translation group pseudo-Euclidean space invariant

2020-10-21abs ↗pdf ↗

Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space IImath.DG

The paper studies mean curvature flow of Lagrangian graphs in pseudo-Euclidean space.

problem Mean curvature flow of Lagrangian graphs in pseudo-Euclidean space.

method Analyzes the parabolic equation and Monge-Ampère type equation, proving smooth solutions and convergence to self-expanding solutions.

result Smooth solutions

u(x,t)

for specific nonlinear equations and convergence to self-expanding solutions.

mean curvature flow Lagrangian graphs pseudo-Euclidean space parabolic equation Monge-Ampère type equation

2024-10-23abs ↗pdf ↗

On Cohomogeneity One Linear Actions On Pseudo-euclidean Space

\mathbb{R}^{p,q}

math.DG

The paper studies cohomogeneity one actions on pseudo-Euclidean space and identifies unique orbit structures.

problem Characterizing cohomogeneity one actions on pseudo-Euclidean spaces.

method Analyzing isometric linear actions of subgroups of the isometry group of

\mathbb{R}^{p,q}

result Identified unique orbit structures of cohomogeneity one actions on

\mathbb{R}^{p,q}

pseudo-Euclidean space cohomogeneity one isometric actions nilpotent factor orbit-equivalence

2019-08-14abs ↗pdf ↗

General Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo- Euclidean Space E42math.DG

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.

2013-02-12abs ↗pdf ↗

Rigidity of spacelike translating solitons in pseudo-Euclidean spacemath.DG

The paper proves rigidity of spacelike translating solitons in pseudo-Euclidean space.

problem Classifying and proving rigidity of spacelike translating solitons in pseudo-Euclidean space.

method Affine technique and classical gradient estimates to classify complete spacelike translating solitons.

result The only complete spacelike translating solitons in pseudo-Euclidean space are the spacelike

m

-planes.

spacelike translating solitons pseudo-Euclidean space rigidity theorem complete spacelike solitons affine technique

2018-04-18abs ↗pdf ↗

Hypersurfaces satisfying

\triangle \vec {H}=λ\vec {H}

in $\mathbb{E}_{\lowercase{s}}^{5}$math.DG

The study examines hypersurfaces in pseudo-Euclidean space with specific curvature properties.

problem Characterizing hypersurfaces with specific curvature conditions in pseudo-Euclidean space.

method Analyzing hypersurfaces satisfying

riangle \vec{H}=λ\vec{H}

\mathbb{E}_{s}^{5}

result Hypersurfaces with diagonal shape operator have constant mean curvature, norm of second fundamental form, and scalar curvature.

Hypersurfaces pseudo-Euclidean space curvature biharmonic shape operator

2024-09-13abs ↗pdf ↗

Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metricmath.DG

The study classifies meridian surfaces with specific curvature properties in a special 4D space.

problem Characterizing surfaces with parallel mean or normalized mean curvature vectors.

method Classification of meridian surfaces based on curvature properties.

result Existence of surfaces with parallel normalized mean curvature but not mean curvature.

Meridian surfaces Curvature Neutral metric Pseudo-Euclidean space Parallel vector field

2016-05-31abs ↗pdf ↗

Theory of Submanifolds, Associativity Equations in 2D Topological Quantum Field Theories, and Frobenius Manifoldsmath.DG

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…

2006-10-30abs ↗pdf ↗

Hyperspheres in Euclidean and Minkowski 4-spaces as almost paracontact almost paracomplex Riemannian manifoldsmath.DG

Study on hyperspheres in 4-spaces as special Riemannian manifolds.

problem Characterizing hyperspheres in Euclidean and Minkowski 4-spaces as specific Riemannian manifolds.

method Constructing and studying hyperspheres in 4-dimensional spaces (Euclidean and pseudo-Euclidean) as almost paracontact almost paracomplex Riemannian manifolds.

result Characterization and geometric properties of these manifolds.

hyperspheres Riemannian manifolds Euclidean pseudo-Euclidean Minkowski

2020-12-01abs ↗pdf ↗

Quasi-minimal Rotational Surfaces in Pseudo-Euclidean Four-dimensional Spacemath.DG

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all q…

2012-10-09abs ↗pdf ↗

Geodesic and billiard flows on quadrics in pseudo-Euclidean spaces: L-A pairs and Chasles theoremnlin.SI

In this article we construct L--A representations of geodesic flows on quadrics and of billiard problems within ellipsoids in the pseudo--Euclidean spaces. A geometric interpretation of the integrability analogous to the classical Chasles theorem for symmetric ellipsoids is given. We also consider a generalization of t…

2014-07-02abs ↗pdf ↗

Canonical Weierstrass Representations for Maximal Space-like Surfaces in $\RR^4_2$math.DG

The paper provides a Weierstrass representation for maximal space-like surfaces in 4D pseudo-Euclidean space.

problem Characterizing maximal space-like surfaces in 4D pseudo-Euclidean space.

method Developed a Weierstrass representation for maximal space-like surfaces using special parameters and holomorphic functions.

result Explicit solutions to the system of natural PDE's are found using holomorphic functions.

Maximal space-like surfaces 4D pseudo-Euclidean space Weierstrass representation PDE system Holomorphic functions

2019-06-24abs ↗pdf ↗

Spacelike Self-Similar Shrinking Solutions of the Mean Curvature Flow in Pseudo-Euclidean Spacesmath.DG

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cas…

2013-07-19abs ↗pdf ↗

Spacelike mean curvature flowmath.DG

Study proves long-term flow for special geometric shapes.

problem Long-term behavior of spacelike surfaces in pseudo-Euclidean space.

method Proves existence and convergence of spacelike mean curvature flow solutions.

result Long-term existence and convergence of spacelike mean curvature flow solutions.

mean curvature flow pseudo-Euclidean space long-time existence convergence

2018-08-06abs ↗pdf ↗

On Flat Pseudo-Euclidean Nilpotent Lie Algebrasmath.DG

The study characterizes flat pseudo-Euclidean Lie algebras and their properties.

problem Characterizing flat pseudo-Euclidean Lie algebras and their properties.

method Using the double extension process and analyzing the center of the Lie algebras.

result All flat pseudo-Euclidean nilpotent Lie algebras of signature

(2,n-2)

can be obtained by the double extension process from flat Lorentzian nilpotent Lie algebras.

Lie algebras nilpotent symmetric bilinear form double extension center

2017-11-18abs ↗pdf ↗

The next variational prolongation of the Euclidean spacemath.DG

The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.

2014-07-17abs ↗pdf ↗

On rotational surfaces in pseudo-Euclidean space

\mathbb{E}^4_t

with pointwise 1-type Gauss mapmath.DG

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain …

2015-08-13abs ↗pdf ↗

Rigity results on

ρ

-Einstein solitons with zero scalar curvaturemath.DG

Study on $ρ$ -Einstein solitons with zero scalar curvature, proving stability and flatness.

problem Characterizing

ρ

-Einstein solitons with specific curvature properties.

method Analyzing

ρ

-Einstein solitons conformal to pseudo-Euclidean spaces with invariant pseudo-orthogonal group.

result Stability and flatness of

ρ

-Einstein solitons with zero scalar curvature.

Einstein solitons pseudo-Euclidean spaces pseudo-orthogonal group zero scalar curvature stability

2021-02-10abs ↗pdf ↗

Invariant Solutions for Gradient Ricci Almost Solitonsmath.DG

The paper identifies invariant solutions for gradient Ricci almost solitons.

problem Understanding invariant solutions for gradient Ricci almost solitons.

method Analyzing conformal metrics invariant under translation and rotation.

result Identified all conformal metrics invariant under translation and rotation as gradient Ricci almost solitons.

gradient Ricci almost solitons invariant metrics translation group rotation pseudo-euclidean space

2017-05-16abs ↗pdf ↗

High codimension mean curvature flow of spacelike-convex submanifolds with one spacelike codimensionmath.DG

The paper studies mean curvature flow of spacelike-convex submanifolds in pseudo-Euclidean space.

problem Mean curvature flow of spacelike-convex submanifolds in pseudo-Euclidean space.

method Analysis of natural curvature pinching and noncollapsing quantities under mean curvature flow.

result The mean curvature flow deforms any initial spacelike-convex submanifold to a point in finite time, and is asymptotic to a shrinking sphere in a maximally spacelike subspace.

mean curvature flow pseudo-Euclidean space spacelike-convex submanifolds finite time asymptotic behavior

2026-02-23abs ↗pdf ↗