Geodesic
A second-order identity for the Riemann tensor and applications
Carlo Alberto Mantica 1   ; Luca Guido Molinari 1
1 Physics Department Università degli Studi di Milano Via Celoria 16 20133 Milano, Italy
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 69-82 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm122-1-7
Keywords: second order differential identity riemann tensor obtained manifold symmetric connection several old differential identities riemann ricci tensors derived applications manifolds recurrent symmetric structures discussed structure k recurrency naturally emerges invariance property old identity due lovelock

Carlo Alberto Mantica  1   ; Luca Guido Molinari  1

1 Physics Department Università degli Studi di Milano Via Celoria 16 20133 Milano, Italy 
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Carlo Alberto Mantica; Luca Guido Molinari. A second-order identity for the Riemann tensor and applications. Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 69-82. doi: 10.4064/cm122-1-7

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