Geodesic complexity of homogeneous Riemannian manifolds

Stephan Mescher; Maximilian Stegemeyer

doi:10.2140/agt.2023.23.2221

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arXiv · 2105.09215

Geodesic complexity of homogeneous Riemannian manifolds

Stephan Mescher·Maximilian Stegemeyer

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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.

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BibTeX RIS

Stephan Mescher, Maximilian Stegemeyer. 2021-05-19. Geodesic complexity of homogeneous Riemannian manifolds. https://doi.org/10.2140/agt.2023.23.2221

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