Hypersurfaces in space forms satisfying some generalized Einstein metric condition

JOURNAL OF GEOMETRY AND PHYSICS

卷:148

Article

Deszcz, Ryszard¹  Glogowska, Malgorzata¹  Zafindratafa, Georges² 

[1] Wroclaw Univ Environm & Life Sci, Dept Math, Grunwaldzka 53, PL-50357 Wroclaw, Poland

[2] Univ Polytech Hauts de France, Lab Math & Applicat Valenciennes, LAMAV ISTV2, F-59313 Le Mt Houy 9, Valenciennes, France

关键词: Einstein manifold;    Quasi-Einstein manifold;    Pseudosymmetry type curvature condition;    Generalized Einstein metric condition;    Warped product manifold;    Hypersurface;   

DOI  :  10.1016/j.geomphys.2019.103562

来源: Elsevier

【 摘 要 】

The difference tensor C.R-R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n >= 4, satisfy the following curvature condition: (*) C.R-R.C= Q(S, C)-(kappa/(n = 1)) Q(g, C). We investigate hypersurfaces M in space forms N satisfying (*). The main result states that if the tensor C.R-R.C of a non-quasi -Einstein hypersurface M in N is a linear combination of the tensors Q(g, C) and Q(S, C) then (*) holds on M. In the case when M is a quasi-Einstein hypersurface in N and some additional assumptions are satisfied then (*) also holds on M. (C) 2019 The Author(s). Published by Elsevier B.V.

【 授权许可】

Free