Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896969 | Journal of Geometry and Physics | 2007 | 7 Pages |
Abstract
Geometrical characterizations are given for the tensor R⋅SR⋅S, where SS is the Ricci tensor of a (semi-)Riemannian manifold (M,g)(M,g) and RR denotes the curvature operator acting on SS as a derivation, and of the Ricci Tachibana tensor ∧g⋅S∧g⋅S, where the natural metrical operator ∧g∧g also acts as a derivation on SS. As a combination, the Ricci curvatures associated with directions on MM, of which the isotropy determines that MM is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on MM, and of which the isotropy determines that MM is Ricci pseudo-symmetric in the sense of Deszcz.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
B. Jahanara, S. Haesen, Z. Sentürk, L. Verstraelen,