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Bull. Korean Math. Soc. 2024; 61(5): 1395-1412
Online first article July 18, 2024 Printed September 30, 2024
https://doi.org/10.4134/BKMS.b230680
Copyright © The Korean Mathematical Society.
On Yau rigidity theorem for submanifolds with parallel mean curvature in a locally symmetric Riemannian manifold
Fei Yang
China University of Mining and Technology
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.
Keywords: Rigidity theorem, parallel mean curvature, locally symmetric Riemannian manifold
MSC numbers: 53C24, 53C40
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