Hypersurfaces in Esn+1 satisfying Δ(H)over-right-arrow = λ(H)over-right-arrow with at most two distinct principal curvatures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:451

Article

Liu, Jiancheng¹  Yang, Chao¹ 

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China

关键词: Pseudo-Euclidean space;    Hypersurface;    Shape operator;    Mean curvature;    Isoparametric;   

DOI  :  10.1016/j.jmaa.2017.01.090

来源: Elsevier

【 摘 要 】

A. Arvanitoyeorgos and G. Kaimakamis proposed in [1] the conjecture that: any hypersurface satisfying Delta(H) over right arrow = lambda(H) over right arrow in pseudo-Euclidean space E-s(n+1) of index s has constant mean curvature. In this paper, we prove that the conjecture is true when the hypersurfaces have at most two distinct principal curvatures. Then, we estimate that constant mean curvature, and give its explicit expression for some special cases. As a result, for that of Lorentzian type hypersurfaces which are not minimal, we prove that it must be isoparametric and give classification results. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free