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arXiv · 2205.13156

On complete hypersurfaces with constant scalar curvature $n(n-1)$ in the unit sphere

Jinchuan Bai·Yong Luo
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Abstract

Let $M^n$ be an $n$-dimensional complete and locally conformally flat hypersurface in the unit sphere $\mathbb{S}^{n+1}$ with constant scalar curvature $n(n-1)$. We show that if the total curvature $\left( \int _ { M } | H | ^ { n } d v \right) ^ { \frac { 1 } { n } }$ of $M$ is sufficiently small, then $M^n$ is totally geodesic.

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Jinchuan Bai, Yong Luo. 2022-05-26. On complete hypersurfaces with constant scalar curvature $n(n-1)$ in the unit sphere. https://arxiv.org/abs/2205.13156

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