On the cut locus of submanifolds of a Finsler manifold
type: Item
instance of: scholarly article
title: On the cut locus of submanifolds of a Finsler manifold
author: Aritra Bhowmick
author: Sachchidanand Prasad
published in: The Journal of Geometric Analysis
publication date: 2024-09-26T00:00:00Z
review text: The authors extend the results of [\textit{S. Basu} and \textit{S. Prasad}, Algebr. Geom. Topol. 23, No. 9, 4185--4233 (2023; Zbl 1534.53021)] to forward complete Finsler manifolds. Their main result is the following: let \((M,F)\) denote a Finsler manifold \(M\) with a forward complete Finsler metric \(F\), and \(N\) a closed submanifold of \(M\). If \(N\) is noncompact, then \(F\) is assumed to be backward complete. If \(\mbox{Cu}(N)\) denotes the cut locus of \(N\), then \(M\setminus \mbox{Cu}(N)\) strongly deformation retracts onto \(N\), and \(M\setminus N\) strongly deformation retracts onto \(\mbox{Cu}(N)\). In addition to these results, the authors give two characterisations of the cut locus; one in terms of the focal locus and the other in terms of the separating set.
reviewed by: Oliver Jones
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 7919162
zbMATH Keywords: Finsler manifolds
zbMATH Keywords: cut locus
zbMATH Keywords: \(N\)-geodesics
zbMATH Keywords: deformation retracts
zbMATH Keywords: focal locus
zbMATH Keywords: separating sets
MaRDI profile type: Publication
cites work: A note on the existence of tubular neighbourhoods on Finsler manifolds and minimization of orthogonal geodesics to a submanifold
cites work: Q3128806
cites work: A connection between cut locus, Thom space and Morse-Bott functions
cites work: Simplicial Structure of the Real Analytic Cut Locus
cites work: Q4091064
cites work: Q5719717
cites work: An asymmetric Arzelà-Ascoli theorem
cites work: Q5808028
cites work: Blaschke Finsler manifolds and actions of projective Randers changes on cut loci
cites work: The cut loci, conjugate loci and poles in a complete Riemannian manifold
cites work: Chern connection of a pseudo-Finsler metric as a family of affine connections
cites work: Corrigendum to ``Chern connection of a pseudo-Finsler metric as a family of affine connections"
cites work: Curvature computations in Finsler geometry using a distinguished class of anisotropic connections
cites work: Geodesics and Jacobi fields of pseudo-Finsler manifolds
cites work: Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds
cites work: Contributions to riemannian geometry in the large
cites work: Connections between differential geometry and topology. I: Simply connected surfaces.
cites work: Connections between differential geometry and topology. II: Closed surfaces.
cites work: Comparison Finsler Geometry
cites work: A class of Riemannian metrics on a manifold
cites work: Q3417869
cites work: Sur les lignes géodésiques des surfaces convexes.
cites work: A sphere theorem for non-reversible Finsler metrics
cites work: Q3260127
cites work: The cut locus and distance function from a closed subset of a Finsler manifold
cites work: Q4888132
cites work: Differential geometry of spray and Finsler spaces
cites work: Ueber diejenigen Punkte auf positiv gekrümmten Flächen, welche die Eigenschaft haben, dass die von ihnen ausgehenden geodätischen Linien nie aufhören, kürzeste Linien zu sein.
cites work: The Conjugate Locus of a Riemannian Manifold
cites work: The cut locus and conjugate locus of a riemannian manifold
cites work: On the covering of a complete space by the geodesics though a point
cites work: Distance function and cut loci on a complete Riemannian manifold
cites work: Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications
cites work: On conjugate points and geodesic loops in a complete Riemannian manifold
DOI: 10.1007/S12220-024-01751-1
description: scientific article; zbMATH DE number 7919162