Report
Geodesic complexity via fibered decompositions of cut loci
| العنوان: | Geodesic complexity via fibered decompositions of cut loci |
|---|---|
| المؤلفون: | Mescher, Stephan, Stegemeyer, Maximilian |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Algebraic Topology, Mathematics - Differential Geometry, 55M30, 53C22 |
| الوصف: | 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. Comment: 22 pages, revised version, to appear in Journal of Applied and Computational Topology |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2206.07691 |
| رقم الانضمام: | edsarx.2206.07691 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |