Natural connections given by general linear and classical connections

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Authors

JANYŠKA Josef

Year of publication 2005
Type Article in Proceedings
Conference Differential Geometry and its Application
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Gauge-natural bundle; natural operator; linear connection; classical connection; reduction theorem
Description We assume a vector bundle $p:\f E\to \f M$ with a general linear connection $K$ and a classical linear connection $\Lam$ on $\f M$. We prove that all classical linear connections on the total space $\f E$ naturally given by $(\Lam, K)$ form a 15-parameter family. Further we prove that all connections on $J^1\f E$ naturally given by $(\Lam, K)$ form a 14-parameter family. Both families of connections are described geometrically.
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