Natural lifts of classical linear connections to the cotangent bundle
Kureš, Miroslav
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Kureš, Miroslav
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Das, Lovejoy S., Nivas, Ram, Nath Pathak, Virendra (2005)
International Journal of Mathematics and Mathematical Sciences
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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).
Miroslav Doupovec (1994)
Archivum Mathematicum
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We determine all first order natural operators transforming –tensor fields on a manifold into –tensor fields on .
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...