New 8D geometry found with non-Einstein metrics.
problem Exploring new 8D geometric structures.
method Cohomogeneity one SU(3)-manifolds and perturbed quaternion-kaehler metrics.
result Found non-Einstein metrics with closed 4-forms.
On-device research index
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.
169,291 papers · 148 categories
Trend · papers per month
48 results for “8D geometry”
HR in 8D encodes unique conformal gravity with negative curvature.
problem Holographic Renormalisation in 8D Einstein Gravity.
method Relating HR to Topological Regularisation and adding the Euler term.
result The unique conformal gravity theory reproduces the polynomial and cancels divergent terms.
The paper studies 8D manifolds with a specific tensor field called a cubic discriminant.
problem Characterizing and understanding 8D Riemannian manifolds with reduced structure groups.
method Introducing an almost quaternion-Hermitian structure and a cubic discriminant tensor field.
result Only two non-flat, integrable examples of these structures are found: quaternion-Kähler symmetric spaces.
Generic smooth boundaries for isoperimetric regions in 8D manifolds.
problem Understanding boundaries of isoperimetric regions in high-dimensional spaces.
method Generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight.
result Smooth nondegenerate boundaries for isoperimetric regions for generic metrics and volumes.
The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.
problem Finding prime closed characteristics on compact star-shaped hypersurfaces in 8D space.
method Proved existence of at least four prime closed characteristics for non-degenerate compact star-shaped hypersurfaces in without prime closed characteristics of Maslov-type index -1.
result Existence of at least four prime closed characteristics on compact star-shaped hypersurfaces in .
Study on harmonic flow of Spin(7)-structures in 8D manifolds.
problem Comparing isometric Spin(7)-structures.
method Developed a notion of harmonicity for Spin(7)-structures and studied the harmonic flow.
result Analytical properties of the harmonic flow of Spin(7)-structures presented.
Novel gauge-theoretic Floer homologies defined for 7, 6, and 5-manifolds.
problem Defining novel gauge-theoretic Floer homologies for different dimensions.
method Topologically-twisted 8d gauge theory on Spin(7)-manifolds.
result Derivation of novel Floer homologies and -categories.
We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.
problem Constructing and understanding conformal gravity actions in different dimensions.
method Streamlined construction of 6D action, proving existence of 8D action, relating to Q-curvature.
result A unique 8D conformal gravity action exists with Einstein metrics as solutions.
New proof of a unique 3-part partition in 8D space.
problem Existence of a non-standard isoperimetric partition in high dimensions.
method Analytical proof showing existence of a specific partition.
result Existence of a non-standard isoperimetric partition in 8D space.
DM approximates submanifolds with error bounds.
problem Understanding the accuracy of Diffusion Maps in embedding submanifolds.
method Deriving geometric properties and deriving bounds on embedding errors.
result Error bounds for DM embeddings and tangent spaces.
This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called "meta-symplectic structure" ass…
Minimal surfaces in 8D smooth and nondegenerate.
problem Generic regularity of minimal hypersurfaces in 8D.
method Analysis of -generic metrics.
result All minimal hypersurfaces are smooth and nondegenerate.
Generic smooth minimal hypersurfaces exist in 8D manifolds.
problem Existence of smooth minimal hypersurfaces in high-dimensional manifolds.
method Global perturbation argument and a novel geometric invariant.
result Generic metrics on 8D manifolds admit smooth minimal hypersurfaces.
Topological Gauge Theories with Sixteen Supercharges: Higher -categorification of Floer Homologieshep-th
Novel -categories derived from gauge theories for manifold homologies.
problem Categorifying manifold homologies via gauge theories.
method 3d and 8d gauged Landau-Ginzburg models, higher -categories.
result Derived novel -categories for various manifold homologies.
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
problem Finding a new 8-dimensional Taub-NUT-like manifold.
method Used harmonic superspace formalism to derive the metric.
result Derived a new 8D Taub-NUT-like metric.
New bounds on shortest geodesic loops on a sphere.
problem Finding shortest geodesic loops on a sphere.
method Analyzing geodesic loops starting and ending at a fixed point on a sphere.
result At any point on a sphere, there are at least two distinct geodesic loops whose lengths are bounded by 8d and 14d.
Formula derived for Spin(7)-structures on 8D manifolds.
problem Deriving the intrinsic torsion for Spin(7)-structures.
method Explicit formula derivation using Levi-Civita and minimal Spin(7)-connections.
result Formula relating intrinsic torsion to Lee form and codifferential components.
Study classifies 8D Lie groups with specific foliations and Hermitian structures.
problem Classifying 8D Lie groups with specific conformal and minimal foliations.
method Investigates left-invariant Hermitian structures on leaves of 8D Lie groups.
result Classifies Lie groups based on the integrability and types of Hermitian structures.
New symmetry found in 8D distribution with 6D square.
problem Discovering new symmetry in geometric distributions.
method Analyzing rank 3 distribution on 8D manifold with growth vector (3,6,8).
result Maximally symmetric rank 3 distribution with 6D square.
Defines hermitian geometry and formulates it in generalised complex geometry.
problem Defines hermitian geometry and formulates it in generalised complex geometry.
method Formulates hermitian geometry in generalised complex geometry.
result Provides explicit formulae for the map to generalised geometry.
Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.
problem Characterize surfaces with constant ratio of principal curvatures in different geometries.
method Differential geometry, line geometry, Lie sphere geometry, ordinary differential equations, algebraic geometry.
result Characterized various types of surfaces like rotational, channel, ruled, helical, and translational.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…
A car as parabolic geometrymath.DG
A car's motion shows flat parabolic geometry.
problem Understanding the geometry of a car's motion.
method Analyzing a car as a nonholonomic system.
result Shows a car's motion as a flat parabolic geometry.
Hessian geometry explains special geometries in theories.
problem Explaining special geometries in theories.
method Formulating theories in terms of Hessian structures.
result Hessian geometry relates special geometries of vector multiplets to hypermultiplet geometries.
Abstract: Surveying aspects of complex dimension two anti-canonical pairs.
problem Smooth topology, algebraic geometry, symplectic geometry, and contact geometry of anti-canonical pairs.
method Survey and review of existing work.
result Survey of various geometric properties of anti-canonical pairs.
Non-lorentzian spacetimesmath.DG
Non-lorentzian geometry reviewed, including Lie algebras and Klein geometries.
problem Understanding non-lorentzian spacetimes.
method Classification and characterization of kinematical Lie algebras and their geometries.
result Characterization of Cartan geometries based on intrinsic torsion.
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
problem Characterizing projective path geometries on surfaces.
method Solving the equivalence problem of sub-Riemannian geometry of signature (1,1) on a contact 3-manifold.
result Characterization of projective path geometries in terms of their chains.
Surveying recent developments in Hitchin moduli space geometry.
problem Understanding the asymptotic geometry of Hitchin moduli space.
method Introduction to Hitchin moduli space and hyperkähler geometry.
result Recent developments in asymptotic geometry of Hitchin moduli space.
New definition of Born geometry connects to known geometries.
problem Defining and understanding Born geometries.
method Using Künneth structures and recursion operators.
result Born connection derived from Künneth connection for integrable geometries.
The paper extends group constructions to coset geometries, creating new ways to combine geometries.
problem Combining and gluing incidence geometries in a general framework.
method Extending classical group-theoretic constructions to coset geometries.
result Provides a general framework for combining or gluing incidence geometries.
New symmetries found in Riemann-Cartan geometries.
problem Investigating symmetries in geometries with curvature and torsion.
method Mathematical tools to determine symmetries and subclasses of geometries.
result Determined all static and stationary spherically symmetric Riemann-Cartan geometries and subclasses with specific symmetries.
We give an introduction to the theory of varieties of minimal rational tangents, emphasizing its aspect as a fusion of algebraic geometry and differential geometry, more specifically, a fusion of Mori geometry of minimal rational curves and Cartan geometry of cone structures.
Convex meets complexmath.CV
Survey explores interactions between convex and complex geometry.
problem Understanding intersections between convex and complex geometry.
method Survey and review of existing literature.
result Demonstrates fascinating interactions between convex and complex geometry.
Geometry of geodesicsmath.DG
Lecture notes on geodesics in differential geometry.
problem Understanding geodesics in differential geometry.
method Expository lecture notes with exercises.
result Explains the geometry of geodesics.
Spin(7) geometry linked to multisymplectic geometry.
problem Understanding Spin(7) structures through multisymplectic geometry.
method Utilized Spin(7) identities to prove non-degeneracy of Cayley four-form in multisymplectic context.
result Spin(7) geometry is a special case of multisymplectic geometry.
Uses Dirac geometry to prove Poisson geometry results.
problem Classical results in Poisson geometry.
method Dirac geometry techniques.
result Proofs of Poisson geometry results.
The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…
Lecture notes on Finslerian geometry.
problem No specific problem stated; covers Finslerian geometry.
method Lecture notes.
result No specific key result mentioned.
Limits of geometriesmath.GT
A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spac…
Introduces logarithmic Cartan geometry on complex manifolds with singularities.
problem Holomorphic Cartan geometry with singularities.
method Definition and study of logarithmic Cartan geometry on complex manifolds with polar part supported on a normal crossing divisor.
result Push-forward of a Cartan geometry constructed using a finite Galois ramified covering is a logarithmic Cartan geometry.
Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometrymath.FA
Paper introduces a generalized Bures-Wasserstein geometry for SPD matrices.
problem Understanding the geometry of SPD matrices for machine learning.
method Proposes a generalized Bures-Wasserstein geometry parameterized by a symmetric positive definite matrix.
result The GBW geometry outperforms the BW geometry in machine learning applications.
The paper proves a new theorem in Riemannian geometry and offers a new proof for Toponogov's theorem in Alexandrov geometry.
problem Proving new theorems in Riemannian and Alexandrov geometries.
method Inspired by the proof of the Schur-Toponogov theorem, a new proof of Toponogov's theorem is provided.
result A new theorem in Riemannian geometry and a new proof of Toponogov's theorem in Alexandrov geometry.
Maps strong Kähler with torsion to Generalised Complex Geometry.
problem Representing strong Kähler with torsion in Generalised Complex Geometry.
method Analogy to Gualtieri map for models.
result Representation of strong Kähler with torsion in Generalised Complex Geometry.
Simplified Beltrami's theorem using geometry.
problem Beltrami's theorem
method Parabolic differential geometry
result Simplified approach to Beltrami's theorem
Talks about new methods in differential geometry.
problem None explicitly stated in the abstract.
method Stresses the neighbor relation as a basic notion.
result Not explicitly stated in the abstract.
Develops Weyl structures for path geometries, simplifying their study.
problem Complexity in studying path geometries using traditional differential geometry methods.
method Defines distinguished connections and Schouten tensor, proving their dependence on line bundle sections.
result Shows a smaller subclass of Weyl structures for path geometries, with interesting connections to BGG sequences.
Surveying probabilistic real algebraic geometry.
problem Classical problems in real algebraic geometry.
method Probabilistic perspective on classical topics.
result Modern approach to Hilbert's Sixteenth Problem.
The study sets limits on the complexity of Klein geometries.
problem Understanding the complexity of Klein geometries.
method Simple upper and lower bounds for the order of Klein geometries.
result Established upper and lower bounds for the order of Klein geometries.