Geodesic complexity via fibered decompositions of cut loci

Autor:	Mescher, Stephan, Stegemeyer, Maximilian
Rok vydání:	2022
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology Mathematics - Differential Geometry 55M30 53C22
Druh dokumentu:	Working Paper
Popis:	The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of cut loci over whose components the tangent cut loci fiber in a convenient way. We establish a new upper bound for geodesic complexity in terms of such decompositions. As an application, we obtain estimates for the geodesic complexity of certain classes of homogeneous manifolds. In particular, we compute the geodesic complexity of complex and quaternionic projective spaces with their standard symmetric metrics. Comment: 22 pages, revised version, to appear in Journal of Applied and Computational Topology
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.07691 Zobrazit plný text záznamu View this record from Arxiv