On the parallel transport of the Ricci curvatures


Jahanara B., Haesen S., Sentuerk Z., Verstraelen L.

JOURNAL OF GEOMETRY AND PHYSICS, vol.57, no.9, pp.1771-1777, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 9
  • Publication Date: 2007
  • Doi Number: 10.1016/j.geomphys.2007.02.008
  • Title of Journal : JOURNAL OF GEOMETRY AND PHYSICS
  • Page Numbers: pp.1771-1777

Abstract

Geometrical characterizations are given for the tensor R.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 boolean AND(g).S, where the natural metrical operator boolean AND(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. (c) 2007 Elsevier B.V. All rights reserved.