Einstein hypersurfaces of mathbbSⁿ \× \ℝ and\n \ℍⁿ \× \ℝ

2019/10/15 by Benedito Leandro, Leandro, Benedito, Romildo Pina +3
Mathematics · #Geometric Analysis and Curvature Flows #Mathematics and Applications #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1910.06930

Abstract

In this paper, we classify the Einstein hypersurfaces of mathbbSⁿ \×\n\ℝ and \ℍⁿ \× \ℝ. We use the characterization\nof the hypersurfaces of mathbbSⁿ \× \ℝ and \ℍⁿ\n\× \ℝ whose tangent component of the unit vector field spanning\nthe factor \ℝ is a principal direction and the theory of\nisoparametric hypersurfaces of space forms to show that Einstein hypersurfaces\nof mathbbSⁿ \× \ℝ and \ℍⁿ \× \ℝ must\nhave constant sectional curvature.\n

Related

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• Hypersurfaces with constant sectional curvature of \Sfⁿ× \R and \Hyⁿ× \R
• Einstein Hypersurfaces of Warped Product Spaces
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