A sharp integral inequality for compact linear Weingarten hypersurfaces
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초록
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 Al\'{\i}as and Mel\'{e}ndez in \cite{Alias:01} for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.
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 Al\'{\i}as and Mel\'{e}ndez in \cite{Alias:01} for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.
참고문헌 (18)
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