Hypersurfaces in space forms satisfying some generalized Einstein metric condition
The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) 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 non-quasi-Einstein 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 quasi-Einstein hypersurface in N and some additional assumptions are satisfied then (A) also holds on M.
- Pub Date:
- October 2018
- Mathematics - Differential Geometry;
- 83C15 (Primary);
- 53C80 (Secondary)
- Key words and phrases: Einstein manifold, quasi-Einstein manifold, pseudosymmetry type curvature condition, generalized Einstein metric condition, warped product manifold, hypersurface. arXiv admin note: text overlap with arXiv:1812.00670