Upper bounds for the critical values of homology classes of loops
| Autor: | Rademacher, Hans-Bert |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a simply-connected $n$-dimensional manifold of positive Ricci curvature $\textrm{Ric} \ge n-1$ has length $\le n \pi.$ Comment: 6 pages, comments are welcome |
| Databáze: | arXiv |
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