Hypersurfaces in space forms satisfying some curvature conditions

JOURNAL OF GEOMETRY AND PHYSICS

卷:99

Article

Deszcz, Ryszard¹  Glogowska, Malgorzata¹  Hotlos, Marian²  Zafindratafa, Georges³ 

[1] Wroclaw Univ Environm & Life Sci, Dept Math, PL-50357 Wroclaw, Poland

[2] Wroclaw Univ Technol, Dept Math, PL-50370 Wroclaw, Poland

[3] Univ Valenciennes & Hainaut Cambresis, Lab Math & Applicat Valenciennes, Lamath ISTV2, F-59313 Valenciennes 9, France

关键词: Generalized Einstein metric condition;    Rater type manifold;    Tachibana tensor;    Austere hypersurface;    Quasi-Einstein hypersurface;    2-quasi-Einstein hypersurface;   

DOI  :  10.1016/j.geomphys.2015.10.010

来源: Elsevier

【 摘 要 】

In Abdalla and Dillen (2002) an example of a non-semisymmetric Ricci-symmetric quasi-Einstein austere hypersurface M isometrically immersed in an Euclidean space was constructed. In this paper we state that, at every point of the hypersurface M, the following generalized Einstein metric curvature condition is satisfied: (*) the difference tensor R. C - C . R and the Tachibana tensor Q(S, C) are linearly dependent. Precisely, (n - 2) (R C - C . R) = Q(S, C) on M. We also prove that non-conformally flat and non-Einstein hypersurfaces with vanishing scalar curvature having at every point two distinct principal curvatures, as well as some hypersurfaces having at every point three distinct principal curvatures, satisfy (*). We present examples of hypersurfaces satisfying (*). (C) 2015 Published by Elsevier B.V.

【 授权许可】

Free