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

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.

preprint2014arXivOpen access
E. PeyghanC. M. ArcuşL. Nourmohammadifar
math.DG
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E. PeyghanC. M. ArcuşL. Nourmohammadifar

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