Displaying similar documents to “Natural transformations of connections on the first principal prolongation”

Classification of principal connections naturally induced on W 2 P E

Jan Vondra (2008)

Archivum Mathematicum

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We consider a vector bundle E → M and the principal bundle P E of frames of E . Let K be a principal connection on P E and let Λ be a linear connection on M . We classify all principal connections on W 2 P E = P 2 M × M J 2 P E naturally given by K and Λ .

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...