Introduction to the theory of semi-holonomic jets. (English) Zbl 0915.58004

Libermann, Paulette

Arch. Math., Brno 33, No. 3, 173-189 (1997).

The author presents a very readable survey of the foundations of the theory of semi-holonomic jets by C. Ehresmann. She starts with the motivation, which goes back to the theory of systems of partial differential equations on a fibered manifold. Then she discusses the affine bundle structure on the semi-holonomic prolongations. The main applications are the curvature of a general connection, the torsion of a connection on the first order frame bundle and the structure function of a \(G\)-structure. Finally, the theory of double vector bundles by J. Pradines and his representation of nonholonomic and semi-holonomic 2-jets in terms of some maps between the second iterated tangent bundles are discussed.

Reviewer: I.Kolář (Brno)

MSC:

58A20	Jets in global analysis
53C05	Connections (general theory)
53C10	\(G\)-structures

Keywords:

non-holonomic jet; semi-holonomic jet; differential system; connection; \(G\)-structure; survey