On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions

Author:

Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Miroslava Petrović-Torgašev, Georges Zafindratafa

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-27 16:00:00

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.

PDF: On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions.pdf