Distributions on manifolds are studied in terms of jets of submanifolds and are interpreted as «pre-connections» or «almost-fibrings»; the associated differential calculus is developed in detail. A comparison with connections on fibred manifolds is analysed. Moreover, «higher order pre-connections», defined as pre-connections dependent on jets of arbitrary order, are introduced and studied. It is shown that infinite jets play an essential role in the associated differential calculus.
Some variations on the notion of connection / M. MODUGNO; A. VINOGRADOV. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 167:(1994), pp. 33-71. [10.1007/BF01760328]
Some variations on the notion of connection
MODUGNO, MARCO;
1994
Abstract
Distributions on manifolds are studied in terms of jets of submanifolds and are interpreted as «pre-connections» or «almost-fibrings»; the associated differential calculus is developed in detail. A comparison with connections on fibred manifolds is analysed. Moreover, «higher order pre-connections», defined as pre-connections dependent on jets of arbitrary order, are introduced and studied. It is shown that infinite jets play an essential role in the associated differential calculus.
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