Riemann compatible tensors

Carlo Alberto Mantica; Luca Guido Molinari

Displaying similar documents to “Riemann compatible tensors”

Scalar differential concomitants of the second order of the metrical tensor in three-dimensional Riemann spaces

M. Lorens (1970)

Annales Polonici Mathematici

Similarity:

Extended Derdziński-Shen theorem for curvature tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

Similarity:

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.

On density concomitants of the covariant curvature tensor in the two- and three-dimensional Riemann space

L. Bieszk, E. Stasiak (1972)

Annales Polonici Mathematici

Similarity:

A second-order identity for the Riemann tensor and applications

Carlo Alberto Mantica, Luca Guido Molinari (2011)

Colloquium Mathematicae

Similarity:

A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity due to Lovelock.