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Gauge natural constructions on higher order principal prolongations

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

Let W m r P be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on W m r P M . We also describe all geometric constructions of classical linear connections on W m r P from principal connections on P → M and rth order linear connections on M.

Gauge natural prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2009)

Annales Polonici Mathematici

The main result is the classification of all gauge bundle functors H on the category m ( G ) which admit gauge natural operators transforming principal connections on P → M into general connections on HP → M. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to HP → P. A special attention is paid to linear connections.

Geometrical aspects of the covariant dynamics of higher order

D. Opris, I. D. Albu (1998)

Czechoslovak Mathematical Journal

We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra, [7]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations.

Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles

Marcella Palese, Ekkehart Winterroth (2005)

Archivum Mathematicum

We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The proof is based on a global decomposition of the variational Lie derivative of the generalized Euler-Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that...

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