Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A SHARP INTEGRAL INEQUALITY FOR COMPACT LINEAR WEINGARTEN HYPERSURFACES

  • de Lima, Henrique F. (Departamento de Matematica Universidade Federal de Campina Grande) ;
  • dos Santos, Fabio R. (Departamento de Matematica Universidade Federal de Pernambuco) ;
  • Rocha, Lucas S. (Departamento de Matematica Universidade Federal de Campina Grande)
  • Received : 2021.06.27
  • Accepted : 2022.02.24
  • Published : 2022.05.31
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Abstract

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.

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Acknowledgement

The authors would like to thank the referee for reading the manuscript in great detail and for his/her valuable suggestions and useful comments which improved the paper.

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