On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions
Differential Geometry
2023-06-30 v1
Abstract
The difference tensor R.C-C.R of a semi-Riemannian manifold (M,g), dim M > 3, formed by its Riemannian-Christoffel curvature tensor R and the Weyl conformal curvature tensor C, under some assumptions, can be expressed as a linear combination of (0,6)-Tachibana tensors Q(A,T), where A is a symmetric (0,2)-tensor and T a generalized curvature tensor. These conditions form a family of generalized Einstein metric conditions. In this survey paper we present recent results on manifolds and submanifolds, and in particular hypersurfaces, satisfying such conditions.
Keywords
Cite
@article{arxiv.2306.16518,
title = {On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions},
author = {Ryszard Deszcz and Małgorzata Głogowska and Marian Hotloś and Miroslava Petrović-Torgašev and Georges Zafindratafa},
journal= {arXiv preprint arXiv:2306.16518},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2302.09387