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arXiv · 2409.07607

On The Triviality Of $m$-Modified Conformal Vector Fields

Rahul Poddar·Ramesh Sharma
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Abstract

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.

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Rahul Poddar, Ramesh Sharma. 2024-09-11. On The Triviality Of $m$-Modified Conformal Vector Fields. https://arxiv.org/abs/2409.07607

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