TY - JOUR

T1 - On the parallel transport of the Ricci curvatures

AU - Jahanara, B.

AU - Haesen, S.

AU - Sentürk, Z.

AU - Verstraelen, L.

PY - 2007/8

Y1 - 2007/8

N2 - Geometrical characterizations are given for the tensor R {dot operator} S, where S is the Ricci tensor of a (semi-)Riemannian manifold (M, g) and R denotes the curvature operator acting on S as a derivation, and of the Ricci Tachibana tensor∧g {dot operator} S, where the natural metrical operator∧g also acts as a derivation on S. As a combination, the Ricci curvatures associated with directions on M, of which the isotropy determines that M is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on M, and of which the isotropy determines that M is Ricci pseudo-symmetric in the sense of Deszcz.

AB - Geometrical characterizations are given for the tensor R {dot operator} S, where S is the Ricci tensor of a (semi-)Riemannian manifold (M, g) and R denotes the curvature operator acting on S as a derivation, and of the Ricci Tachibana tensor∧g {dot operator} S, where the natural metrical operator∧g also acts as a derivation on S. As a combination, the Ricci curvatures associated with directions on M, of which the isotropy determines that M is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on M, and of which the isotropy determines that M is Ricci pseudo-symmetric in the sense of Deszcz.

KW - Parallel transport

KW - Ricci pseudo-symmetric

KW - Ricci tensor

UR - http://www.scopus.com/inward/record.url?scp=34248576266&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2007.02.008

DO - 10.1016/j.geomphys.2007.02.008

M3 - Article

AN - SCOPUS:34248576266

SN - 0393-0440

VL - 57

SP - 1771

EP - 1777

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 9

ER -