2018/10/02 by Ryszard Deszcz, Malgorzata Glogowska, Małgorzata Głogowska +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B20 #msc:53B25 #msc:53B30 #msc:53B50 #msc:53C25 #msc:53C35 #msc:53C40 #msc:53C80 #msc:83C15
paper · pdf · doi:10.48550/arxiv.1810.01402
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
arxiv created 2019/03/02 · arxiv updated 2019/03/06
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.