Double Affine Bundles

Details Double Affine Bundles Double Affine Bundles

2009-04-14

arxiv.org/abs/0904.2095v2

J. Geom. Phys 60 (2010), 581-598

Mathematics

Differential Geometry

30 pages, minor corrections - an extended version of a version to appear in J. Geom. Phys

Scientific paper

10.1016//j.geomphys.2009.12.008

A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation and basic examples come from Analytical Mechanics, where double affine bundles have been recognized as a proper geometrical tool in a frame-independent description of many important systems. Different approaches to the (special) double affine bundles are compared and carefully studied together with the problems of double vector bundle models and hulls, duality, and relations to associated phase spaces, contact structures, and other canonical constructions.

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