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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.07607 |
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| _version_ | 1866910601306963968 |
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| author | Poddar, Rahul Sharma, Ramesh |
| author_facet | Poddar, Rahul Sharma, Ramesh |
| contents | We prove that a compact Riemannian manifold $M$ does not admit any non-trivial $m$-modified homothetic vector fields. In the corresponding case of an $m$-modified conformal vector field $V$, we establish an inequality that implies the triviality of $V$. Further, we demonstrate that an affine Killing $m$-modified conformal vector field on a non-compact Riemannian manifold $M$ must be trivial. Finally, we show that an $m$-modified gradient conformal vector field is trivial under the assumptions of polynomial volume growth and convergence to zero at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On The Triviality Of $m$-Modified Conformal Vector Fields Poddar, Rahul Sharma, Ramesh Differential Geometry 53C21, 53C25 We prove that a compact Riemannian manifold $M$ does not admit any non-trivial $m$-modified homothetic vector fields. In the corresponding case of an $m$-modified conformal vector field $V$, we establish an inequality that implies the triviality of $V$. Further, we demonstrate that an affine Killing $m$-modified conformal vector field on a non-compact Riemannian manifold $M$ must be trivial. Finally, we show that an $m$-modified gradient conformal vector field is trivial under the assumptions of polynomial volume growth and convergence to zero at infinity. |
| title | On The Triviality Of $m$-Modified Conformal Vector Fields |
| topic | Differential Geometry 53C21, 53C25 |
| url | https://arxiv.org/abs/2409.07607 |