Hypersurfaces in space forms satisfying some generalized Einstein metric condition
Abstract
The difference tensor C.R  R.C of Einstein manifolds, some quasiEinstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R  R.C = Q(S,C)  (k /(n1)) Q(g,C). We investigate hypersurfaces M in space forms N satisfying (A). The main result states that if the tensor C.R  R.C of a nonquasiEinstein hypersurface M in N is a linear combination of the tensors Q(g,C) and Q(S,C) then (A) holds on M. In the case when M is a quasiEinstein hypersurface in N and some additional assumptions are satisfied then (A) also holds on M.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.01402
 arXiv:
 arXiv:1810.01402
 Bibcode:
 2018arXiv181001402D
 Keywords:

 Mathematics  Differential Geometry;
 53B20;
 53B25;
 53B30;
 53B50;
 53C35;
 83C15 (Primary);
 53C25;
 53C40;
 53C80 (Secondary)
 EPrint:
 Key words and phrases: Einstein manifold, quasiEinstein manifold, pseudosymmetry type curvature condition, generalized Einstein metric condition, warped product manifold, hypersurface. arXiv admin note: text overlap with arXiv:1812.00670