Combinatorial differential geometry and ideal Bianchi-Ricci identities

Details Combinatorial differential geometry and ideal Bianchi-Ricci identities Combinatorial differential geometry and ideal Bianchi-Ricci identities

2008-09-06

arxiv.org/abs/0809.1158v1

Mathematics

Differential Geometry

31 pages

Scientific paper

We apply the graph complex method to vector fields depending naturally on a set of vector fields and a linear symmetric connection. We characterize all possible systems of generators for such vector-field valued operators including the classical ones given by normal tensors and covariant derivatives. We also describe the size of the space of such operators and prove the existence of an `ideal' basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi-Ricci identities without the correction terms.

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