On iteration of higher order jets and prolongation of connections

Miroslav Doupovec; Włodzimierz M. Mikulski

Displaying similar documents to “On iteration of higher order jets and prolongation of connections”

On prolongation of higher order connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We describe all bundle functors G admitting natural operators transforming rth order holonomic connections on a fibered manifold Y → M into rth order holonomic connections on GY → M. For second order holonomic connections we classify all such natural operators.

Connections on higher order principal prolongations

Vašík, Petr

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Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.

Prolongation of second order connections to vertical Weil bundles

Antonella Cabras, Ivan Kolář (2001)

Archivum Mathematicum

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$ . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$ -field for another Weil algebra $B$ and of its $A$ -prolongation.

Higher order jet involution

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Czechoslovak Mathematical Journal

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We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.