Reduction theorems for general linear connections

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Authors

JANYŠKA Josef

Year of publication 2004
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Gauge-natural bundle; natural operator; linear connection; reduction theorem
Description 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.
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