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Displaying similar documents to “Nonlinear connections and semisprays on tangent manifolds.”

On the iterated absolute differentiation on some functional bundles

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.

Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec, Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -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 F -vertical bundles. We also present some examples and applications.