Displaying similar documents to “Prolongation of second order connections to vertical Weil bundles”

Second order connections on some functional bundles

Antonella Cabras, Ivan Kolář (1999)

Archivum Mathematicum

Similarity:

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...

Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec, Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

Similarity:

Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to F -vertical bundles. We also present some examples and applications.

Natural lifting of connections to vertical bundles

Kolář, Ivan, Mikulski, Włodzimierz M.

Similarity:

One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order ( r , s , q ) on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold Y into connections on an arbitrary vertical bundle over Y . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over Y under which every natural operator in question has finite order. ...