Classification of Hypersurfaces with Two Distinct Principal Curvatures and Closed Moebius Form in ${\mathbb{S}}^{m+1}$

Abstract

Let $x$ be an $m$-dimensional umbilic-free hypersurface in an $(m+1)$-dimensional unit sphere ${\mathbb{S}}^{m+1}(m\ge 3)$. One of important questions is to classify hypersurfaces with two distinct principal curvatures. In this paper, we classify and explicitly express the hypersurfaces with two distinct principal curvatures and closed Moebius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.

This paper has been withdrawn by the author due to a crucial error

Cited by in corpus (2)

• Deformation of Hypersurfaces Preserving the Moebius Metric and a Reduction Theorem
• A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in ${\mathbb{S}}^{n+1}$