On the Cut Locus of Submanifolds of a Finsler Manifold
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913462474506240 |
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| author | Bhowmick, Aritra Prasad, Sachchidanand |
| author_facet | Bhowmick, Aritra Prasad, Sachchidanand |
| contents | In this article, we investigate the cut locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. We explore the deformation and characterization of the cut locus, extending the results of Basu and the second author (\emph{Algebraic and Geometric Topology}, 2023). Given a submanifold $N$, we consider an $N$-geodesic loop as an $N$-geodesic starting and ending in $N$, possibly at different points. This class of geodesics were studied by Omori (\emph{Journal of Differential Geometry}, 1968). We obtain a generalization of Klingenberg's lemma for closed geodesics (\emph{Annals of Mathematics}, 1959) for $N$-geodesic loops in the reversible Finsler setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11045 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Cut Locus of Submanifolds of a Finsler Manifold Bhowmick, Aritra Prasad, Sachchidanand Differential Geometry Primary: 53C22, 53B40, Secondary: 53C60 In this article, we investigate the cut locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. We explore the deformation and characterization of the cut locus, extending the results of Basu and the second author (\emph{Algebraic and Geometric Topology}, 2023). Given a submanifold $N$, we consider an $N$-geodesic loop as an $N$-geodesic starting and ending in $N$, possibly at different points. This class of geodesics were studied by Omori (\emph{Journal of Differential Geometry}, 1968). We obtain a generalization of Klingenberg's lemma for closed geodesics (\emph{Annals of Mathematics}, 1959) for $N$-geodesic loops in the reversible Finsler setting. |
| title | On the Cut Locus of Submanifolds of a Finsler Manifold |
| topic | Differential Geometry Primary: 53C22, 53B40, Secondary: 53C60 |
| url | https://arxiv.org/abs/2307.11045 |