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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.

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48 results for “geodesic spaces”

Spaces of Geodesics: Products, Coverings, Connectednessmath.DG

We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient condition…

1995-01-24abs ↗pdf ↗

Spaces of Geodesic Triangulations Are Cellsmath.GT

Proving geodesic triangulation spaces are Euclidean.

problem Proving spaces of geodesic triangulations are homeomorphic to Euclidean spaces.

method Proposing an approach to prove homeomorphism using negative curvature surfaces.

result Spaces of geodesic triangulations are homeomorphic to Euclidean spaces.

geodesic triangulations negative curvature Euclidean spaces homeomorphism

2022-04-22abs ↗pdf ↗

Two-step homogeneous geodesics in some homogeneous Finsler manifoldsmath.DG

The paper extends two-step homogeneous geodesics to homogeneous Finsler spaces.

problem Extending two-step homogeneous geodesics to Finsler spaces.

method Providing sufficient conditions for

(α,β)

spaces and decomposable cubic spaces to have two-step Finsler geodesic orbit spaces.

result Presented examples of two-step Finsler geodesic orbit spaces.

two-step geodesics Finsler spaces homogeneous spaces geodesic orbit spaces

2021-09-06abs ↗pdf ↗

Totally geodesic submanifolds in products of rank one symmetric spacesmath.DG

Classifies totally geodesic submanifolds in symmetric spaces.

problem Classifying submanifolds in symmetric spaces.

method Classification of totally geodesic submanifolds in products of rank one symmetric spaces.

result Infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces.

totally geodesic submanifolds symmetric spaces classification Hermitian symmetric spaces

2022-05-29abs ↗pdf ↗

Geodesic orbit spaces of compact Lie groups of rank twomath.DG

Researchers classify geodesic orbit spaces for compact Lie groups of rank two.

problem Identifying geodesic orbit spaces for compact Lie groups of specific rank.

method Classification of simply connected geodesic orbit spaces where G is a compact Lie group of rank two.

result Only certain spheres and projective spaces, with metrics induced from Hopf fibrations, are geodesic orbit spaces for compact Lie groups of rank two.

geodesic orbit spaces compact Lie groups rank two spheres projective spaces

2020-08-31abs ↗pdf ↗

Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spacesmath.DG

Geodesic orbit metrics proven on specific homogeneous spaces.

problem Geodesic orbit metrics on homogeneous spaces.

method Using strongly isotropy irreducible spaces and proving natural reductivity.

result Geodesic orbit metrics are naturally reductive on constructed homogeneous spaces.

geodesic orbit metrics homogeneous spaces strongly isotropy irreducible natural reductivity

2020-12-13abs ↗pdf ↗

Geodesics on an ellipsoid in Minkowski spacemath.DG

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and space-like geodesics and invariant 1-form on the space of null geodesics. We prove a…

2007-05-01abs ↗pdf ↗

Simple closed geodesics on regular tetrahedra in spaces of constant curvaturemath.MG

Survey on geodesics on tetrahedra in curved spaces.

problem Understanding geodesics on tetrahedra in curved spaces.

method Analyzing geodesics on regular tetrahedra in spaces of constant curvature.

result Results on the behavior of simple closed geodesics.

geodesics tetrahedra curved spaces constant curvature

2022-12-05abs ↗pdf ↗

Totally geodesic submanifolds in exceptional symmetric spacesmath.DG

Classifies totally geodesic submanifolds in exceptional symmetric spaces.

problem Classifying totally geodesic submanifolds in exceptional symmetric spaces.

method Classification and introduction of an invariant (Dynkin index) for totally geodesic embeddings.

result Existence of a totally geodesic submanifold of minimal codimension with specific properties.

totally geodesic submanifolds exceptional symmetric spaces Dynkin index index conjecture

2022-02-22abs ↗pdf ↗

Homogeneous geodesics in homogeneous Finsler spacesmath.DG

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogen…

2007-06-24abs ↗pdf ↗

No Periodic normal Geodesics in

J^k(\mathbb{R},\mathbb{R}^n)

math.DS

Study shows no periodic geodesics in jet space.

problem Existence of periodic geodesics in jet space.

method Characterization and classification of subRiemannian geodesics.

result No periodic geodesics found in the space of k-jets.

jet space geodesics Hamiltonian flow subRiemannian geometry Carnot group

2022-05-12abs ↗pdf ↗

Totally geodesic submanifolds of Teichmuller spacemath.DS

We show that any totally geodesic submanifold of Teichmuller space of dimension greater than one covers a totally geodesic subvariety, and only finitely many totally geodesic subvarieties of dimension greater than one exist in each moduli space.

2017-02-10abs ↗pdf ↗

Horoboundary and rigidity of filling geodesic currentsmath.GT

New metric on geodesic currents connects different surface genera.

problem Understanding geodesic currents on surfaces of varying genera.

method Introducing a new asymmetric metric on the space of projective filling geodesic currents.

result Metric spaces of projective filling geodesic currents for surfaces of different genera are not isometric.

geodesic currents projective spaces metric spaces rigidity hyperbolic surfaces

2026-01-05abs ↗pdf ↗

Finite Energy Geodesic Rays in Big Cohomology Classesmath.DG

New metric spaces for geodesic rays in cohomology classes.

problem Constructing geodesic rays in cohomology classes with finite energy.

method Introduced a chordal metric and proved geodesic properties.

result Found a characterization of geodesic rays in terms of test curves.

cohomology classes geodesic rays finite energy metric spaces chordal metric

2024-06-11abs ↗pdf ↗

Geodesic graphs for geodesic orbit Finsler

(α,β)

metrics on spheresmath.DG

Geodesic graphs for special Finsler metrics on spheres are studied.

problem Characterizing geodesic orbit Finsler metrics on spheres.

method Explicit constructions and group extensions.

result Not all projective spaces admit invariant Finsler metrics.

geodesic orbit Finsler metrics spheres projective spaces Riemannian geodesic orbit

2023-03-16abs ↗pdf ↗

Geodesic loops on tetrahedra in spaces of constant sectional curvaturemath.DG

Geodesic loops on tetrahedra are studied in spherical and hyperbolic spaces.

problem Characterize geodesic loops on tetrahedra in different types of spaces.

method Analytical proofs for spherical and hyperbolic spaces.

result Existence and properties of geodesic loops on tetrahedra in various spaces.

geodesic loops tetrahedra spherical space hyperbolic space constant sectional curvature

2023-08-03abs ↗pdf ↗

Geodesic simplices of pseudo-hyperbolic spacemath.GT

Geodesic simplices in pseudo-hyperbolic space get a cohomological treatment.

problem Understanding geodesic simplices in pseudo-hyperbolic space.

method Cohomological interpretation and necessary/sufficient condition formulation.

result Every ideal geodesic polytope in

(2,2)

pseudo-hyperbolic space has finite volume.

pseudo-hyperbolic space geodesic simplices cohomology finite volume

2026-05-07abs ↗pdf ↗

On the structure of geodesic orbit Riemannian spacesmath.DG

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic submanifolds that inherit the property to be geodesic orbit. For a given geodesic…

2016-11-03abs ↗pdf ↗

Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifoldsmath.DG

Study geodesic orbit metrics in quaternionic Stiefel manifolds.

problem Characterize geodesic orbit spaces in quaternionic Stiefel manifolds.

method Analyze homogeneous Riemannian spaces

(M=G/H,g)

with geodesics as orbits of subgroups.

result Identify conditions for $(\Sp(n)/\Sp(n_1) imes \cdots imes \Sp(n_s), g)$ to be a geodesic orbit space.

geodesic orbit metrics homogeneous bundles quaternionic Stiefel manifolds Riemannian spaces semisimple groups

2021-03-04abs ↗pdf ↗

On a class of geodesic orbit spaces with abelian isotropy subgroupmath.DG

Classifies geodesic orbit spaces with abelian isotropy subgroups.

problem Characterizing and classifying geodesic orbit spaces with specific isotropy subgroups.

method Simplified study of geodesic orbit metrics on G/S by reducing to submanifolds and generalized flag manifolds, using properties of root systems.

result Geodesic orbit spaces of the form (G/S,g) are naturally reductive.

geodesic orbit spaces naturally reductive compact Lie groups abelian isotropy root systems

2020-04-26abs ↗pdf ↗

On the geodesics of homogeneous Finsler spaces with some special

(α, β)

-metricsmath.DG

In this paper, we study geodesics and geodesic vectors for homogeneous exponential Finsler space and homogeneous infinite series Finsler space. Further, we find necessary and sufficient condition for a non-zero vector in these homogeneous spaces to be a geodesic vector.

2018-01-31abs ↗pdf ↗

Compact geodesic orbit spaces with a simple isotropy groupmath.DG

The paper classifies geodesic orbit spaces with simple isotropy groups.

problem Classifying geodesic orbit spaces with simple isotropy groups.

method Classifying

G

-naturally reductive and

G

-geodesic orbit metrics on

M

result Classification of geodesic orbit spaces with simple isotropy groups.

geodesic orbit homogeneous space simple isotropy naturally reductive geodesic orbit metrics

2020-09-14abs ↗pdf ↗

Closed geodesics on compact Lorentzian solvmanifoldsmath.DG

Study geodesics on compact Lorentzian solvmanifolds, finding conditions for closedness.

problem Conditions for closed geodesics on compact Lorentzian solvmanifolds.

method Analyzing geodesics on Lorentzian homogeneous spaces of solvable Lie groups.

result Conditions for every lightlike geodesic to be closed on quotient spaces.

geodesics Lorentzian solvmanifolds closed geodesics compact spaces

2024-11-21abs ↗pdf ↗

Divergent geodesics, ambiguous closed geodesics and the binary additive divisor problemmath.DG

Study geodesics in curved spaces, counts ambiguous paths, confirms number theory conjectures.

problem Counting ambiguous geodesics in curved spaces.

method Asymptotic formula for common perpendiculars in negatively curved spaces, applying to modular orbifolds and number fields.

result Confirms and extends Motohashi's conjecture on binary additive divisor problem.

geodesics curved spaces asymptotic formula modular orbifold number fields

2024-09-26abs ↗pdf ↗

Gromov-Hausdorff distances from simply connected geodesic spaces to the circlemath.MG

Circle's metric is at least π/4 away from any simply connected geodesic space.

problem Comparing simply connected geodesic spaces to the circle.

method Using Gromov-Hausdorff distance and topological properties.

result The Gromov-Hausdorff distance between circle and any simply connected geodesic space is at least π/4.

Gromov-Hausdorff distance circle geodesic space simply connected topology

2024-04-08abs ↗pdf ↗

Quantizing Geodesics in Kähler and Sasaki Geometrymath.DG

Quantizes geodesics in Kähler and Sasaki geometry.

problem Quantize geodesics in Kähler and Sasaki spaces.

method Classical Fubini-Study map and quantization procedure.

result Proves conditions for geodesics in Kähler potentials.

geodesics Kähler geometry Sasaki geometry quantization

2026-03-02abs ↗pdf ↗

Finite sample bounds for barycenter estimation in geodesic spacesmath.ST

Estimates barycenter in geodesic spaces with finite sample bounds.

problem Estimating the barycenter of a distribution in geodesic spaces.

method Finite sample error bounds, Hoeffding- and Bernstein-type concentration inequalities, efficient algorithms.

result Statistical guarantees for efficient barycenter computation.

barycenter geodesic spaces finite sample bounds concentration inequalities

2025-02-19abs ↗pdf ↗

On the almost sure spiraling of geodesics in CAT(0) spacesmath.DS

Geodesics spiral around compact subsets in CAT(0) spaces.

problem Understanding geodesic spiraling in CAT(0) spaces.

method Logarithm law-type result for geodesics in quotients of rank one CAT(0) spaces.

result Proved logarithm law for geodesic spiraling in certain CAT(0) spaces.

CAT(0) spaces geodesics spiraling logarithm law quotients

2025-09-13abs ↗pdf ↗

Geodesics in generalized Finsler spaces: singularities in dimension twomath.DG

We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized…

2015-07-23abs ↗pdf ↗

Hopf fibrations and totally geodesic submanifoldsmath.DG

Classifies totally geodesic submanifolds in Hopf-Berger spheres.

problem Classifying totally geodesic submanifolds in Hopf-Berger spheres.

method Investigates Hopf-Berger spheres, a special family of homogeneous spaces diffeomorphic to spheres constructed via Hopf fibrations.

result Discovered intriguing examples of totally geodesic submanifolds, including isometric submanifolds of real projective spaces and non-congruent submanifolds.

Hopf fibrations totally geodesic submanifolds homogeneous spaces spheres positive curvature

2023-02-23abs ↗pdf ↗

Complete Geodesic Metrics in Big Classesmath.DG

The paper defines a complete geodesic metric for high energy spaces in Kähler manifolds.

problem Defining a metric for high energy spaces in Kähler manifolds.

method Endowing the high energy space with a metric that makes it a complete geodesic metric space.

result The geodesic metric space

(\mathcal{E}^{p}(X,θ), d_{p})

is uniformly convex for

p > 1

Kähler manifolds geodesic metrics high energy spaces uniform convexity

2024-01-03abs ↗pdf ↗

Geodesic Mappings and Einstein Spacesmath.DG

In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.

2012-01-13abs ↗pdf ↗

Submanifolds of a complex space form, whose geodesics lie in 1 - dimensional complex submanifoldsmath.DG

It is proved, that if M is a connected, complete submanifold of a complex space form N and each geodesic of M lies in an 1-dimensional totally geodesic complex submanifold of N, then M is totally geodesic in N and is a real space form or a complex space form.

2009-12-21abs ↗pdf ↗

Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifoldsmath.DG

Study geodesic orbit metrics on specific homogeneous spaces.

problem Characterize geodesic orbit spaces in a class of homogeneous bundles.

method Analyze geodesic orbit spaces of compact Lie groups with semisimple subgroups.

result Identify conditions for a metric to be geodesic orbit.

geodesic orbit homogeneous space Stiefel manifold Lie group Riemannian metric

2021-03-04abs ↗pdf ↗

Geodesic orbit Finsler metrics on Euclidean spacesmath.DG

A Finsler space $(M,F)$ is called a geodesic orbit space if any geodesic of constant speed is the orbit of a one-parameter subgroup of isometries of $(M, F)$ . In this paper, we study Finsler metrics on Euclidean spaces which are geodesic orbit metrics. We will show that, in this case $(M, F)$ is a fiber bundle over a s…

2018-07-09abs ↗pdf ↗

Totally geodesic submanifolds of the homogeneous nearly Kähler 6-manifolds and their G2-conesmath.DG

Classifies totally geodesic submanifolds in specific geometric spaces.

problem Identifying totally geodesic submanifolds in homogeneous nearly Kähler 6-manifolds and their G2-cones.

method Developed new techniques for studying totally geodesic submanifolds in analytic Riemannian manifolds, homogeneous spaces, and Riemannian cones.

result Obtained a classification of totally geodesic submanifolds in homogeneous nearly Kähler 6-manifolds and their G2-cones.

totally geodesic submanifolds homogeneous nearly Kähler 6-manifolds G2-cones new techniques analytic Riemannian manifolds

2024-11-18abs ↗pdf ↗

Comparison and Rigidity Theorems for geodesic curvatures in two dimensional Alexandrov spacesmath.DG

Study geodesic curvature in 2D Alexandrov spaces, generalizing results from spaces with curvature above.

problem Geodesic curvature in Alexandrov spaces with curvature below.

method Comparison and rigidity theorems for geodesic curvatures.

result Generalized known results for geodesic curvature in spaces with curvature above.

Alexandrov spaces geodesic curvature comparison theorems rigidity theorems curvature below

2026-01-07abs ↗pdf ↗

Homogeneous spaces with geodesic orbit Riemannian metrics and with integrable invariant distributionsmath.DG

Study finds homogeneous spaces with geodesic orbits but no integrable distributions.

problem Characterizing homogeneous spaces with specific geometric properties.

method Examined Lie groups with compact stabilizers and classified spaces based on geodesic orbits and integrable distributions.

result Identified homogeneous spaces with geodesic orbits but lacking integrable invariant distributions.

Homogeneous spaces Geodesic orbits Invariant distributions Lie groups Invariant metrics

2026-01-12abs ↗pdf ↗

Two robots moving geodesically on a treemath.GT

Researchers analyze geodesic complexity in robot paths on tree graphs.

problem Understanding optimal paths for robots on tree graphs.

method Examined geodesic complexity in ordered and unordered configuration spaces of graphs in

\ell_1

and

\ell_2

metrics, finding explicit geodesics and families.

result Geodesic complexity matches topological complexity in all cases studied.

robotics geodesic complexity topological complexity tree graphs configuration spaces

2020-06-26abs ↗pdf ↗

Rigidity of negatively curved geodesic orbit Finsler spacesmath.DG

We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic Finsler space with strictly negative flag curvature must be a non-compact Riemannian symmetric space of rank one.

2016-04-26abs ↗pdf ↗

Hyperbolicity via Geodesic Stabilitymath.MG

A geodesic $g$ is Morse, for every $L \geq 1, A \geq 0$ there exists a $C=C_g(L,A)$ such that any $(L,A)$ -quasi-geodesic connecting two points on $g$ stays $C$ -close to $g$ . The Morse lemma implies that in a hyperbolic space every geodesic is Morse. Here we prove the converse: If a homogeneous proper geodesic space is …

2015-04-26abs ↗pdf ↗

Thurston geodesics: no backtracking and active intervalsmath.GT

Develops active intervals for geodesics in Teichmüller space.

problem Understanding geodesics in Teichmüller space with no backtracking.

method Defines active intervals for subsurfaces along geodesics in Thurston metric.

result Active intervals represent reparametrized quasi-geodesics in curve graphs with bounded movement outside.

Thurston geodesics Teichmüller space active intervals quasi-geodesics curve graphs

2024-08-03abs ↗pdf ↗

On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spacesmath.DG

Recently, it is shown that each regular homogeneous Finsler space $M$ admits at least one homogeneous geodesic through any point $o\in M$ . The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous $(α,β)$ -spaces, specially, homogeneous Kropina spaces. We show that any homoge…