Displaying similar documents to “Combinatorics of curvature, and the Bianchi identity.”

On the second order absolute differentiation

Cabras, Antonella, Kolář, Ivan

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In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)]...

Special tangent valued forms and the Frölicher-Nijenhuis bracket

Antonella Cabras, Ivan Kolář (1993)

Archivum Mathematicum

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We define the tangent valued C -forms for a large class of differential geometric categories. We deduce that the Frölicher-Nijenhuis bracket of two tangent valued C -forms is a C -form as well. Then we discuss several concrete cases and we outline the relations to the theory of special connections.

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.