Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$

Benedito Leandro; Romildo Pina; João Paulo dos Santos

Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$

Differential Geometry 2019-10-16 v1

Authors: Benedito Leandro , Romildo Pina , João Paulo dos Santos

Abstract

In this paper, we classify the Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ . We use the characterization of the hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ whose tangent component of the unit vector field spanning the factor $\mathbb{R}$ is a principal direction and the theory of isoparametric hypersurfaces of space forms to show that Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ must have constant sectional curvature.

Keywords

einstein hypersurfaces product spaces principal direction isoparametric hypersurfaces space forms constant sectional curvature

Cite

@article{arxiv.1910.06930,
  title  = {Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$},
  author = {Benedito Leandro and Romildo Pina and João Paulo dos Santos},
  journal= {arXiv preprint arXiv:1910.06930},
  year   = {2019}
}

Einstein hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$

Abstract

Keywords

Cite

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