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Constructions on second order connections

J. Kurek, W. M. Mikulski (2007)

Annales Polonici Mathematici

We classify all m , n -natural operators : J ² J ² V A transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections ( Γ ) : V A Y J ² V A Y on the vertical Weil bundle V A Y M corresponding to a Weil algebra A.

Contact elements on fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2003)

Czechoslovak Mathematical Journal

For every product preserving bundle functor T μ on fibered manifolds, we describe the underlying functor of any order ( r , s , q ) , s r q . We define the bundle K k , l r , s , q Y of ( k , l ) -dimensional contact elements of the order ( r , s , q ) on a fibered manifold Y and we characterize its elements geometrically. Then we study the bundle of general contact elements of type μ . We also determine all natural transformations of K k , l r , s , q Y into itself and of T ( K k , l r , s , q Y ) into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms...

Distinguished geodesics and jacobi fields on first order jet spaces

Vladimir Balan, Nicoleta Voicu (2004)

Open Mathematics

In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.

Double linear connections

Alena Vanžurová (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Double vector spaces

Alena Vanžurová (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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