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arXiv · 1410.8804

Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality

E. Peyghan·C. M. Arcuş·L. Nourmohammadifar
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Abstract

Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of exterior differential calculus for generalized Lie algebroids, a covariant derivative for exterior forms of a (dual) vector bundle is introduced. Using this covariant derivative, the complete lift of an arbitrary section of a (dual) vector bundle is discovered. A theory of Legendre type and Legendre duality between vertical and complete lifts is presented. Finally, a duality between Lie algebroids structures is developed.

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E. Peyghan, C. M. Arcuş, L. Nourmohammadifar. 2014-10-05. Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality. https://arxiv.org/abs/1410.8804

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