A second-order identity for the Riemann tensor and applications

Abstract

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend 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 by Lovelock.

16 pages

Cited by in corpus (7)

• Weakly Z symmetric manifolds
• Weyl compatible tensors
• Curvature Properties of Gödel metric
• Energy conditions for a $(WRS{)}_4$ spacetime in $F(R)$-gravity
• Impact of curvature based geometric constraints on $F(R)$ theory
• On pseudo-Riemannian manifolds with recurrent concircular curvature tensor
• On conformally recurrent manifolds of dimension greater than 4