On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions

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 symmetr...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Deszcz, Ryszard, Głogowska, Małgorzata, Hotloś, Marian, Petrović-Torgašev, Miroslava, Zafindratafa, Georges
Format: Article
Language:English
Subjects:
Curvature
Hyperspaces
Manifolds (mathematics)
Mathematical analysis
Riemann manifold
Tensors
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Summary: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.
ISSN:2331-8422