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

2014/10/05 by E. Peyghan, Peyghan, E., Constantin M. Arcuş +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1410.8804

openalex publication_date 2014/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• The geometry of Lie algebroids and its applications to optimal control

Related

• Algebraic constructions in the category of vector bundles
• Intersection between the geometry of generalized Lie algebroids and some\n aspects of interior and exterior differential systems
• Differential calculus on a Lie algebroid and Poisson manifolds
• The metrizability of the generalized tangent bundle of dual of a vector\n bundle
• Algebraic Constructions in the Category of Lie Algebroids