Displaying similar documents to “The Cotton Tensor and the Ricci Flow”

The Evolution of the Weyl Tensor under the Ricci Flow

Giovanni Catino, Carlo Mantegazza (2011)

Annales de l’institut Fourier

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We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.

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.