Displaying similar documents to “Geometric characterization of the homogeneity of continua with microstructure.”

Second order connections on some functional bundles

Antonella Cabras, Ivan Kolář (1999)

Archivum Mathematicum

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We study the second order connections in the sense of C. Ehresmann. On a fibered manifold Y , such a connection is a section from Y into the second non-holonomic jet prolongation of Y . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on Y , which are deduced in the first part of...

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)]...

On jets of surfaces.

Fernando Etayo Gordejuela (1991)

Collectanea Mathematica

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We study the 2-jet bundle of mappings of the real plane into a manifold. We shall prove that there exists an imbedding of this 2-jet bundle into a suitable first order jet bundle, in such a way that its image is the set of fixed points of a canonical automorphism of the biggest jet bundle.