Results 1 to 10 of about 165 (117)
Riemannian Manifolds, Closed Geodesic Lines, Topology and Ramsey Theory
MathematicsWe applied the Ramsey analysis to the sets of points belonging to Riemannian manifolds. The points are connected with two kinds of lines: geodesic and non-geodesic.
Edward Bormashenko
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Rank inequality in homogeneous Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 This is a survey on some recent progress in homogeneous Finsler geometry. Three topics are discussed, the classification of positively curved homogeneous Finsler spaces, the geometric and topological properties of homogeneous Finsler spaces satisfying $K\
Ming Xu
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Geodesic Mappings of Semi-Riemannian Manifolds with a Degenerate Metric
Mathematics, 2022 This article introduces the concept of geodesic mappings of manifolds with idempotent pseudo-connections. The basic equations of canonical geodesic mappings of manifolds with completely idempotent pseudo-connectivity and semi-Riemannian manifolds with a ...
Igor G. Shandra, Josef Mikeš
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Геодезичні відображення коспактних квазі-ейнштейнових просторів
Pracì Mìžnarodnogo Geometričnogo Centru, 2021 The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector. Previously the authors defined three types of these spaces. In the present paper it is proved that there are no quasi-Einstein spaces of special type.
Володимир Анатолійович Кіосак +2 more
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On the equidistribution of closed geodesics and geodesic nets
Transactions of the American Mathematical Society, 2023 We show that given a closed n n -manifold
Li, Xinze, Staffa, Bruno
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Forum of Mathematics, Sigma, 2021 Many natural real-valued functions of closed curves are known to extend continuously to the larger space of geodesic currents. For instance, the extension of length with respect to a fixed hyperbolic metric was a motivating example for the development of
Dídac Martínez-Granado +1 more
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Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics [PDF]
Science China Mathematics, 2015 If all prime closed geodesics on $(S^n,F)$ with an irreversible Finsler metric $F$ are irrationally elliptic, there exist either exactly $2\left[\frac{n+1}{2}\right]$ or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler $(S^3,F)$ if any prime closed geodesic has non ...
Duan, HuaGui, Liu, Hui
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Geodesic Mappings onto Generalized m-Ricci-Symmetric Spaces
Mathematics, 2022 In this paper, we study geodesic mappings of spaces with affine connections onto generalized 2-, 3-, and m-Ricci-symmetric spaces. In either case, the main equations for the mappings are obtained as a closed system of linear differential equations of the
Volodymyr Berezovski +3 more
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Connecting and Closed Geodesics of a Kropina Metric
Advanced Nonlinear Studies, 2021 We prove some results about existence of connecting and closed geodesics in a manifold endowed with a Kropina metric. These have applications to both null geodesics of spacetimes endowed with a null Killing vector field and Zermelo’s navigation problem ...
Caponio Erasmo +3 more
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A proof of a trace formula by Richard Melrose
Advanced Nonlinear Studies, 2023 The goal of this article is to give a new proof of the wave trace formula proved by Richard Melrose in an impressive article. This trace formula is an extension of the Chazarain-Duistermaat-Guillemin trace formula (denoted as “CDG trace formula” in this ...
Colin de Verdière Yves
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