Prolongation of second order connections to vertical Weil bundles. (English) Zbl 1090.58003

Cabras, Antonella; Kolář, Ivan

Arch. Math., Brno 37, No. 4, 333-347 (2001).

A section of the second non-holonomic jet prolongation of a fibred manifold is defined to be a second order connection. In the paper prolongations of second order connections on a fibred manifold to its vertical bundle determined by a Weil algebra \(A\) are studied. The properties of the absolute differentiation with respect to prolongated connection are studied as well.

Reviewer: Josef Janyška (Brno)

MSC:

58A20	Jets in global analysis
53C05	Connections (general theory)

Keywords:

non-holonomic jet; Weil bundle; second order connection; prolongation of connection