Extended Derdziński–Shen theorem for curvature tensors

Volume 128 / 2012

Carlo Alberto Mantica, Luca Guido Molinari Colloquium Mathematicum 128 (2012), 1-6 MSC: Primary 53B20; Secondary 53B21. DOI: 10.4064/cm128-1-1

Abstract

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.

Authors

  • Carlo Alberto ManticaI.I.S. Lagrange
    Via L. Modignani 65
    20161, Milano, Italy
    e-mail
  • Luca Guido MolinariPhysics Department
    Università degli Studi di Milano
    and
    I.N.F.N. sezione di Milano
    Via Celoria 16
    20133, Milano, Italy
    e-mail

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