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PARA-BLASCHKE ISOPARAMETRIC HYPERSURFACES IN A UNIT SPHERE Sn + 1(1)*

Published online by Cambridge University Press:  30 March 2012

SHICHANG SHU  and
BIANPING SU
SHICHANG SHU
Affiliation:
Institute of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000 Shaanxi, P.R. China e-mail: shushichang@126.com
BIANPING SU
Affiliation:
Department of Science, Xi'an University of Architecture and Technology, Xi'an 710055 ShaanxiP.R. China e-mail: subianping@126.com
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Abstract

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Let A = ρ2∑i,jAijθi ⊗ θj and B = ρ2∑i,jBij θi ⊗ θj be the Blaschke tensor and the Möbius second fundamental form of the immersion x. Let D = A + λB be the para-Blaschke tensor of x, where λ is a constant. If x: Mn ↦ Sn + 1(1) is an n-dimensional para-Blaschke isoparametric hypersurface in a unit sphere Sn + 1(1) and x has three distinct Blaschke eigenvalues one of which is simple or has three distinct Möbius principal curvatures one of which is simple, we obtain the full classification theorems of the hypersurface.

Keywords

53A3053B25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 579 - 597
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

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