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 -