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arXiv · 1308.3086

Lifting geometric objects to the dual of the first jet bundle of a bundle fibred over R

Willy Sarlet·Goedele Waeyaert
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Abstract

We study natural lifting operations from a bundle E over R to the dual bundle of its first-jet bundle. The main purpose is to define a complete lift of a type (1,1) tensor field on E and to understand all features of its construction. Various other lifting operations of tensorial objects on E are needed for that purpose. We prove that the complete lift of a type (1,1) tensor with vanishing Nijenhuis torsion gives rise to a Poisson-Nijenhuis structure on the dual of the first-jet bundle, and discuss in detail how the construction of associated Darboux-Nijenhuis coordinates can be carried out.

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Willy Sarlet, Goedele Waeyaert. 2013-08-14. Lifting geometric objects to the dual of the first jet bundle of a bundle fibred over R. https://doi.org/10.1016/j.geomphys.2013.08.009

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