Möbius isoparametric hypersurfaces with three distinct principal curvatures, II

Zejun Hu and Shujie Zhai

Vol. 249 (2011), No. 2, 343–370

DOI: 10.2140/pjm.2011.249.343

Abstract

Using the method of moving frames and the algebraic techniques of T. E. Cecil and G. R. Jensen that were developed while they classified the Dupin hypersurfaces with three principal curvatures, we extend Hu and Li’s main theorem in Pacific J. Math. 232:2 (2007), 289–311 by giving a complete classification for all Möbius isoparametric hypersurfaces in 𝕊ⁿ⁺¹ with three distinct principal curvatures.

Keywords

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

Mathematical Subject Classification 2000

Primary: 53A30

Secondary: 53B25

Milestones

Received: 1 January 2010

Revised: 13 March 2010

Accepted: 8 June 2010

Published: 1 February 2011