A Characterization of Linear Weingarten Submanifolds in a Semi-Riemannian Space Form with Arbitrary Index

Abstract

In this paper, we deal with the spacelike linear Weingarten submanifolds with parallel normalized mean curvature vector in an \((n+p)\)-dimensional semi-Riemannian space form \(N^{n+p}_{q}(c)\) of constant sectional curvature c with index q, where \(1\le q\le p\). In this setting, we obtain an important inequality and apply some appropriated generalized maximum principles to a suitable Cheng–Yau-modified operator to obtain some characterizations of the linear Weingarten submanifolds.

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Acknowledgements

The authors wish to thank the referee for very useful suggestions and comments for improving the original version of the paper. The first author is supported by the NSFC (No. 11801246) and the General Project for Department of Liaoning Education (No. LJC201901), and the second author is supported by Liaoning Provincial Science and Technology Department Project (No. 2020-MS-340), and Liaoning BaiQianWan Talents Program.

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Correspondence to Dan Yang.

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Yang, D., Fu, Y. A Characterization of Linear Weingarten Submanifolds in a Semi-Riemannian Space Form with Arbitrary Index. Mediterr. J. Math. 17, 200 (2020). https://doi.org/10.1007/s00009-020-01641-0

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Keywords

  • Generalized maximum principles
  • linear Weingarten submanifolds
  • spacelike submanifolds

Mathematics Subject Classification

  • Primary 53C42
  • Secondary 53A10