Geodesic complexity of homogeneous Riemannian manifolds

Autor:	Mescher, Stephan, Stegemeyer, Maximilian
Rok vydání:	2021
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology Mathematics - Differential Geometry 55M30 53C22
Zdroj:	Algebr. Geom. Topol. 23 (2023) 2221-2270
Druh dokumentu:	Working Paper
DOI:	10.2140/agt.2023.23.2221
Popis:	We study the geodesic motion planning problem for complete Riemannian manifolds and investigate their geodesic complexity, an integer-valued isometry invariant introduced by D. Recio-Mitter. Using methods from Riemannian geometry, we establish new lower and upper bounds on geodesic complexity and compute its value for certain classes of examples with a focus on homogeneous Riemannian manifolds. Methodically, we study properties of stratifications of cut loci and use results on their structures for certain homogeneous manifolds obtained by T. Sakai and others. Comment: Revised version, 35 pages, 1 figure. To appear in Algebraic & Geometric Topology
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.09215 Zobrazit plný text záznamu View this record from Arxiv