K-symplectic formalism on Lie algebroids

Abstract

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson sigma models.

35 pages

References in corpus (8)

• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Lagrangian submanifolds and dynamics on Lie algebroids
• Classical field theory on Lie algebroids: Variational aspects
• Discrete Lagrangian field theories on Lie groupoids
• Gravity from Lie algebroid morphisms
• Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory
• Euler-Poincare reduction for discrete field theories

Cited by in corpus (4)

• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Symmetries of second order differential equations on Lie algebroids
• Symmetries, Newtonoids vector fields and conservation laws in the Lagrangian $k$-symplectic formalism
• Reduced classical field theories. k-cosymplectic formalism on Lie algebroids