文献类型：期刊文献

英文题名：Hypersurfaces Satisfying τ₂(φ) = ητ(φ) in Pseudo-Riemannian Space Forms

作者：Du, Li[1];Zhang, Juan[1];Xie, Xun[2]

第一作者：Du, Li

通信作者：Zhang, J[1]

机构：[1]Gansu Univ Chinese Med, Dept Sci Teaching, Dingxi Campus, Dingxi 743000, Gansu, Peoples R China;[2]Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China

第一机构：甘肃中医药大学定西校区

通信机构：[1]corresponding author), Gansu Univ Chinese Med, Dept Sci Teaching, Dingxi Campus, Dingxi 743000, Gansu, Peoples R China.|[10735c915ec3c5bdc1d21]甘肃中医药大学定西校区;[10735]甘肃中医药大学;

年份：2017

卷号：20

期号：2

外文期刊名：MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000401270000015)】；

基金：L. Du was supported by the Talent Engineering Funds (2012-2017) and the Major Project (No. TD2016ZD06). J. Zhang was supported by the Talent Engineering Funds (2013-2017) and the General Project (No. TD2016YB08).

语种：英文

外文关键词：Pseudo-Riemannian space forms; Hypersurfaces; Diagonalizable shape operator; Principal curvatures

摘要：In this paper, we derived the equations for the hypersurface M-r(n) of a pseudo-Riemannian space form N-q(n+1) (c) to satisfy tau(2)(phi) = eta tau(phi) (eta a constant) with tau(phi) and tau(2)(phi) be the tension and bitension fields of M-r(n). As applications, we prove that a hypersurface M-r(n) satisfying tau(2)(phi) = eta tau(phi) in N-q(n+1) (c) has constant mean curvature, under the assumption that M-r(n) has diagonalizable shape operator with at most three distinct principal curvatures. Then, using this result, we classify partially such hypersurface. We also make a preliminary study of hypersurfaces satisfying tau(2)(phi) = f tau(phi) with f be function.