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On Yau rigidity theorem for submanifolds with parallel mean curvature in a locally symmetric Riemannian manifold

Fei Yang
대한수학회 (The Korean Mathematical Society)|2024.09|대한수학회보 (Bulletin of the KMS)|제61권 제5호|pp. 1395-1412|DOI 10.4134/BKMS.b230680

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키워드

Rigidity theoremparallel mean curvaturelocally symmetric Riemannian manifold
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초록

In this paper, we investigate the rigidity problem of compact submanifolds with parallel mean curvature in a locally symmetric Riemannian manifold. Firstly, we prove a Yau type rigidity theorem for compact hypersurfaces with parallel mean curvature in a locally symmetric Riemannian manifold. Then we extend the theorem to the case of higher codimension.

Abstract

In this paper, we investigate the rigidity problem of compact submanifolds with parallel mean curvature in a locally symmetric Riemannian manifold. Firstly, we prove a Yau type rigidity theorem for compact hypersurfaces with parallel mean curvature in a locally symmetric Riemannian manifold. Then we extend the theorem to the case of higher codimension.

참고문헌 (19)

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