Reduction theorems for general linear connections. (English) Zbl 1108.53016

Janyška, Josef

Differ. Geom. Appl. 20, No. 2, 177-196 (2004).

Summary: It is well known that natural operators of linear symmetric connections on manifolds and of classical tensor fields can be factorized through the curvature tensors, the tensor fields and their covariant differentials. We generalize this result for general linear connections on vector bundles. In this gauge-natural situation we need an auxiliary linear symmetric connection on the base manifold. We prove that natural operators defined on the spaces of general linear connections on vector bundles, on the spaces of linear symmetric connections on base manifolds and on certain tensor bundles can be factorized through the curvature tensors of linear and classical connections, the tensor fields and their covariant differentials with respect to both connections.

MSC:

53C05	Connections (general theory)
58A20	Jets in global analysis

Keywords:

Gauge-natural bundle; Natural operator; Linear connection; Classical connection; Reduction theorem

References:

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