2022/06/15 by Stephan Mescher, Maximilian Stegemeyer, Mescher, Stephan +1
Mathematics · Physics and Astronomy · #53C22 #55M30 #Advanced Differential Geometry Research #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.2206.07691
openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.