Ercüment Ortaçgil (1998)
Archivum Mathematicum
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We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann -connection.
Josef Janyška, Marco Modugno (1996)
Archivum Mathematicum
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All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
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 , such a connection is a section from into the second non-holonomic jet prolongation of . 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 , which are deduced in the first part of...