Weyl's Theory in the Generalized Lie Algebroids Framework

Abstract

The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical $\left(\rho ,\eta \right)$-system with respect to a $(\rho ,\eta )$-spray, the Berwald $(\rho ,\eta )$-derivative operator and its mixed curvature, we obtain main results to conceptualize the Weyl's method in this general framework. Finally, we obtain two new results of Weyl type for the geometry of mechanical $\left(\rho ,\eta \right)$-systems.

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Cited by in corpus (3)

• Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality
• Remarks on generalized Lie algebroids and related concepts
• Generalized Lie Algebroids - Examples by Distinguished Lie Algebroids with Applications to Optimal Control