Bull. Korean Math. Soc.
Published online May 12, 2022
Copyright © The Korean Mathematical Society.
Henrique de Lima, Fábio dos Santos, and Lucas Rocha
Federal University of Campina Grande, Federal University of Pernambuco
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 curvature, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in reference  for the case of hypersurfaces with constant scalar curvature in the Euclidean round sphere.
Keywords: Locally symmetric Einstein manifold; compact linear Weingarten hypersurfaces; totally umbilical hypersurfaces; isoparametric hypersurfaces
MSC numbers: Primary: 53C42; Secondary: 53C24 and 53C40.
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