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Natural connections given by general linear and classical connections

Josef Janyška
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Abstract

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

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Josef Janyška. 2004-10-21. Natural connections given by general linear and classical connections. https://arxiv.org/abs/math/0410461

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