Natural connections given by general linear and classical connections
  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. 
Josef Jany\v{s}ka