In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler–Lagrange geodesics and Wong’s fractional equations are derived. Many interesting consequences are explored.

In this paper we start developing the so-called Klein’s formalism on dual Lie algebroids. The nonlinear connection associated to a regular section is naturally obtained. Particularly, this connection is found for the Hamiltonian case. Mathematics Subject Classification: 17B66, 53C05.

The "odd transgression" introduced by the authors in an earlier article is applied to construct and study inverse image functor theory of Courant algebroids.

We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford – Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off–diagonal metrics and linear and nonlinear connections define different types of Finsler, Lagrange and/or Riemann–Cartan spaces. A generalization to spinor fields and D...

For any regular Courant algebroid, we construct a characteristic class à la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Ševera class (in H DR(M)). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form (in H(g...