English

A second-order identity for the Riemann tensor and applications

Differential Geometry 2012-02-16 v2

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.

Keywords

Cite

@article{arxiv.0802.0650,
  title  = {A second-order identity for the Riemann tensor and applications},
  author = {Carlo Alberto Mantica and Luca Guido Molinari},
  journal= {arXiv preprint arXiv:0802.0650},
  year   = {2012}
}

Comments

16 pages

R2 v1 2026-06-21T10:09:45.841Z