Prolongations of tensor fields and connections to the Weil bundles (Q1589098)

Let \(M^A_n\) be the Weil bundle of an \(n\)-dimensional differentiable manifold \(M_n\) for an arbitrary local algebra \(A\). The author studies the lifts to \(M^A_n\) of some geometric objects defined on \(M_n\), such as: functions, tensor fields linear connections. The lift of a linear connection considered by the author is, in fact, the synectic lift in the sense of A. P. Shirokov. The author shows that a synectic lift of a linear connection is the realization of a holomorphic connection on \(M^A_n\).