Horizontal lift of connections to a natural vector bundle. (English) Zbl 0646.53028

Gancarzewicz, J.

Differential geometry, Proc. 5th Int. Colloq., Santiago de Compostela/Spain 1984, Res. Notes Math. 131, 318-341 (1985).

[For the entire collection see Zbl 0637.00004.]
The author first studies the basic properties of lifts of vector fields from the base manifold to a vector bundle endowed with a linear connection. Having a vector bundle E associated to the rth order frame bundle F rM, a linear connection on E can be induced from a principal connection on F rM. The main result of the paper is that every principal connection on F rM determines a linear connection on TE\(\to E\) characterized by certain simple geometric conditions. Some geometric properties of the latter connection are also deduced.

Reviewer: I.Kolář

MSC:

53C05

Connections (general theory)

Keywords:

lifts of vector fields; vector bundle; frame bundle; linear connection

Citations:

Zbl 0637.00004