A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in \mathbbSⁿ⁺¹

2017/09/06 by Lin, Limiao, Li, Tongzhu, Wang, Changping
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.01658

Abstract

In this paper, we study conformally flat hypersurfaces of dimension n(≥ 4) in \mathbbSⁿ⁺¹ using the framework of Möbius geometry. First, we classify and explicitly express the conformally flat hypersurfaces of dimension n(≥ 4) with constant Möbius scalar curvature under the Möbius transformation group of \mathbbSⁿ⁺¹. Second, we prove that if the conformally flat hypersurface with constant Möbius scalar curvature R is compact, then R=(n-1)(n-2)r², ~~0

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