Extended Derdziński–Shen theorem for curvature tensors
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 1-6 MSC: Primary 53B20; Secondary 53B21. DOI: 10.4064/cm128-1-1
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.