Geodesic complexity of homogeneous Riemannian manifolds

IF 0.6 3区 数学 Q3 MATHEMATICS Algebraic and Geometric Topology Pub Date : 2021-05-19 DOI:10.2140/agt.2023.23.2221
Stephan Mescher, Maximilian Stegemeyer
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引用次数: 1

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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齐次黎曼流形的测地线复杂度
研究了完全黎曼流形的测地线运动规划问题,研究了由D. Recio-Mitter引入的整数值等距不变量测地线复杂度。本文以齐次黎曼流形为研究对象,利用黎曼几何的方法,建立了新的测地线复杂度的下界和上界,并计算了其值。系统地研究了切位点的分层性质,并将T. Sakai等人得到的切位点结构的结果应用于某些齐次流形。
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来源期刊
CiteScore
1.10
自引率
14.30%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.
期刊最新文献
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