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International Journal of Mathematics and Mathematical Sciences
Volume 2014 (2014), Article ID 398746, 10 pages
http://dx.doi.org/10.1155/2014/398746
Research Article

Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in

School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China

Received 21 January 2014; Accepted 17 March 2014; Published 14 April 2014

Academic Editor: Ricardo Estrada

Copyright © 2014 Junfeng Chen and Shichang Shu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be an -dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere , and let and be the Blaschke tensor and the Möbius second fundamental form of , respectively. We define a symmetric tensor which is called the para-Blaschke tensor of , where is a constant. An eigenvalue of the para-Blaschke tensor is called a para-Blaschke eigenvalue of . The aim of this paper is to classify the oriented hypersurfaces in with two distinct para-Blaschke eigenvalues under some rigidity conditions.