Extended Derdziński-Shen theorem for curvature tensors
Carlo Alberto Mantica, Luca Guido Molinari (2012)
Colloquium Mathematicae
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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.