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arXiv · 2203.09712

Hypersurfaces with Constant Mean Curvatures on Finsler manifolds

Yali Chen·Qun He·Yantong Qian
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Abstract

In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a homothetic navigation, which means that some geometric properties of submanifolds are the same. Finally, we deduce a Heintze-Karcher type inequality and prove an Alexandrov type theorem in special Finsler spaces.

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Yali Chen, Qun He, Yantong Qian. 2022-03-18. Hypersurfaces with Constant Mean Curvatures on Finsler manifolds. https://arxiv.org/abs/2203.09712

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