Extended Derdzinski-Shen theorem for the Riemann tensor
Differential Geometry
2012-10-31 v1 Mathematical Physics
math.MP
Abstract
We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"), typical of some well known differential structures.
Cite
@article{arxiv.1101.4157,
title = {Extended Derdzinski-Shen theorem for the Riemann tensor},
author = {Carlo Alberto Mantica and Luca Guido Molinari},
journal= {arXiv preprint arXiv:1101.4157},
year = {2012}
}
Comments
5 pages