Connection theory on differentiable fibre bundles: A concise introduction.
Iliev, Bozhidar Z. (2006)
International Journal of Mathematics and Mathematical Sciences
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Iliev, Bozhidar Z. (2006)
International Journal of Mathematics and Mathematical Sciences
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Antonella Cabras, Ivan Kolář (1997)
Archivum Mathematicum
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We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.
Miroslav Doupovec, Włodzimierz M. Mikulski (2005)
Archivum Mathematicum
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Let be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to -vertical bundles. We also present some examples and applications.
Antonella Cabras, Ivan Kolář (1995)
Czechoslovak Mathematical Journal
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