×

A second-order identity for the Riemann tensor and applications. (English) Zbl 1218.53016

Summary: 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.

MSC:

53B20 Local Riemannian geometry
PDFBibTeX XMLCite
Full Text: DOI arXiv