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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