A SECOND-ORDER IDENTITY FOR THE RIEMANN TENSOR AND APPLICATIONS

作者：Mantica Carlo Alberto^*; Molinari Luca Guido

来源：Colloquium Mathematicum, 2011, 122(1): 69-82.

DOI：10.4064/cm122-1-7

• Riemann tensor
• symmetric manifold
• recurrent manifold
• weakly Ricci symmetric manifold

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

• 出版日期2011