We extend a remarkable theorem of Derdzinski 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.
Extended Derdzinski-Shen theorem for curvature tensors / C. A. Mantica, L. G. Molinari. - In: COLLOQUIUM MATHEMATICUM. - ISSN 0010-1354. - 128:1(2012), pp. 1-6. [10.4064/cm128-1-1]
Extended Derdzinski-Shen theorem for curvature tensors
C.A. Mantica;L.G. MolinariUltimo
2012
Abstract
We extend a remarkable theorem of Derdzinski 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.
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