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

2022/05/26 by Bai, Jinchuan, Luo, Yong
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.13156

Abstract

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

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