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On complete submanifolds with parallel normalized mean curvature in product spaces
Published online by Cambridge University Press: 27 January 2022
Abstract
A Simons type formula for submanifolds with parallel normalized mean curvature vector field (pnmc submanifolds) in the product spaces $M^{n}(c)\times \mathbb {R}$, where
$M^{n}(c)$ is a space form with constant sectional curvature
$c\in \{-1,1\}$, it is shown. As an application is obtained rigidity results for submanifolds with constant second mean curvature.
Keywords
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 2 , April 2022 , pp. 331 - 355
- Copyright
- Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
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