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New results on the theory of connections: systems, overconnections and prolongations. (English) Zbl 0636.53039

Differential geometry and its applications, Proc. Conf., Brno/Czech. 1986, Math. Appl., East Eur. Ser. 27, 243-269 (1987).
[For the entire collection see Zbl 0624.00014.]
The author considers new methods in handling connections on fibred manifolds with possible applications in gauge theories and general relativity. A fibred manifold is a surjective submersion \(p: E\to B\), dim E\(=1+\dim B\). The main notions presented are the following: systems on double fibred manifolds, systems of connections, jet prolongations of the space of connections, overconnections. The systems of overconnections which project on the system of connections itself and on the system of symmetric linear connections of the base space are investigated.
Reviewer: V.Boju

MSC:

53C05 Connections (general theory)
53C80 Applications of global differential geometry to the sciences

Citations:

Zbl 0624.00014