Double structures and jets

Details Double structures and jets Double structures and jets

2011-08-30

arxiv.org/abs/1108.6013v1

Mathematics

Differential Geometry

Based on a talk given at a meeting in Krakow for the eightieth birthday of W. M. Tulczyjew

Scientific paper

We show how the double vector bundle structure of the manifold of double velocities, with its submanifolds of holonomic and semiholonomic double velocities, is mirrored by a structure of holonomic and semiholonomic subgroups in the principal prolongation of the first jet group. We use the actions of these groups to construct holonomic and semiholonomic submanifolds in the manifold of double contact elements, and show that these give rise to affine bundles where a semiholonomic element has well-defined holonomic and curvature components.

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