Möbius isoparametric hypersurfaces with three distinct principal curvatures

Zejun Hu and Deying Li

Vol. 232 (2007), No. 2, 289–311

DOI: 10.2140/pjm.2007.232.289

Abstract

We investigate Möbius isoparametric hypersurfaces in the (n + 1)-Euclidean unit sphere 𝕊ⁿ⁺¹ with three distinct Möbius principal curvatures. As direct consequence of our main result, we establish the complete classification for all such hypersurfaces in 𝕊⁶.

Keywords

Möbius isoparametric hypersurface, Möbius equivalence, Möbius second fundamental form, Möbius metric, Möbius form

Mathematical Subject Classification 2000

Primary: 53A30

Secondary: 53B25

Milestones

Received: 20 August 2006

Revised: 22 December 2006

Accepted: 1 February 2007

Published: 1 October 2007