Geodesic complexity of homogeneous Riemannian manifolds
Geometric Topology
2023-08-02 v4 Algebraic Topology
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2105.09215,
title = {Geodesic complexity of homogeneous Riemannian manifolds},
author = {Stephan Mescher and Maximilian Stegemeyer},
journal= {arXiv preprint arXiv:2105.09215},
year = {2023}
}
Comments
Revised version, 35 pages, 1 figure. To appear in Algebraic & Geometric Topology