Dynamics of the Morse vector field
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911460861411328 |
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| author | Zhang, Yijian |
| author_facet | Zhang, Yijian |
| contents | The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points through orbits and exponential shrinkage of the flow on stable submanifolds. We also find applications in showing some vanishing results of maps or curvature operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of the Morse vector field Zhang, Yijian Differential Geometry The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points through orbits and exponential shrinkage of the flow on stable submanifolds. We also find applications in showing some vanishing results of maps or curvature operators. |
| title | Dynamics of the Morse vector field |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.23268 |