Geodesic
On the iterated absolute differentiation on some functional bundles
Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 23-35
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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.
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.
Classification : 53C05, 58A20
Keywords: bundle of smooth maps; connection on a functional bundle; iterated absolute differentiation; iterated 2-jet; Ricci identity 
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Cabras, Antonella; Kolář, Ivan. On the iterated absolute differentiation on some functional bundles. Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 23-35. http://geodesic.mathdoc.fr/item/ARM_1997_33_1-2_a4/

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