Hypersurfaces with Constant Mean Curvatures on Finsler manifolds
Differential Geometry
2024-03-14 v4
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.
Keywords
Cite
@article{arxiv.2203.09712,
title = {Hypersurfaces with Constant Mean Curvatures on Finsler manifolds},
author = {Yali Chen and Qun He and Yantong Qian},
journal= {arXiv preprint arXiv:2203.09712},
year = {2024}
}
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19 pages