Einstein Hypersurfaces of Sn X R and Hn X R
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY(2021)
Abstract
In this paper, we classify the Einstein hypersurfaces of S-n x R and H-n x R. We use the characterization of the hypersurfaces of S-n x R and H-n x R whose tangent component of the unit vector field spanning the factor R is a principal direction and the theory of isoparametric hypersurfaces of space forms to show that Einstein hypersurfaces of S-n x R and H-n x R must have constant sectional curvature.
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Key words
Hypersurfaces in product spaces,Einstein manifolds,Constant sectional curvature
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