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

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)


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