We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-1,
author = {Carlo Alberto Mantica and Luca Guido Molinari},
title = {Extended Derdzi\'nski-Shen theorem for curvature tensors},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {1-6},
zbl = {1269.53018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-1}
}
Carlo Alberto Mantica; Luca Guido Molinari. Extended Derdziński-Shen theorem for curvature tensors. Colloquium Mathematicae, Tome 126 (2012) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-1/