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

Abstract

Using the covariant derivative for exterior forms of a (dual) vector bundle, the complete lift of an arbitrary section of a (dual) vector bundle is discovered. A theory of Legendre type and Legendre duality between vertical lifts and between complete lifts are presented. Finally, a duality between Lie algebroids structures is developed

Keywords

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

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