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Einstein Hypersurfaces of $$\mathbb {S}^n \times \mathbb {R}$$ and $$\mathbb {H}^n \times \mathbb {R}$$
Bulletin of the Brazilian Mathematical Society, New Series ( IF 0.9 ) Pub Date : 2020-06-30 , DOI: 10.1007/s00574-020-00216-7
Benedito Leandro , Romildo Pina , João Paulo dos Santos

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.

中文翻译:

$$\mathbb {S}^n \times \mathbb {R}$$ 和 $$\mathbb {H}^n \times \mathbb {R}$$ 的爱因斯坦超曲面

在本文中,我们对 $\mathbb{S}^n \times \mathbb{R}$ 和 $\mathbb{H}^n \times \mathbb{R}$ 的爱因斯坦超曲面进行分类。我们使用 $\mathbb{S}^n \times \mathbb{R}$ 和 $\mathbb{H}^n \times \mathbb{R}$ 的超曲面的表征,其单位向量场的切分量跨越因子 $\mathbb{R}$ 是一个主方向,空间形式的等参超曲面理论表明,$\mathbb{S}^n \times \mathbb{R}$ 和 $\mathbb{H 的爱因斯坦超曲面}^n \times \mathbb{R}$ 必须具有恒定的截面曲率。
更新日期:2020-06-30
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