Riemann compatible tensors
Differential Geometry
2012-11-30 v2 Mathematical Physics
math.MP
Abstract
Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity of the new "Codazzi deviation tensor" with a geometric significance. Examples are given of manifolds with Riemann-compatible tensors, in particular those generated by geodesic mapping. Compatibility is extended to generalized curvature tensors with an application to Weyl's tensor and general relativity.
Cite
@article{arxiv.1204.1211,
title = {Riemann compatible tensors},
author = {C. A. Mantica and L. G. Molinari},
journal= {arXiv preprint arXiv:1204.1211},
year = {2012}
}
Comments
12 pages