Compact cosymplectic manifolds of positive constant phi-sectional curvature.
Geometric characterization of the homogeneity of continua with microstructure.
Dynamical connections and non-autonomous lagrangian systems
Lifts of derivations to the frame bundle
Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies
We present a general geometrical theory of uniform bodies which includes three-dimensional Cosserat bodies, rods and shells as particular cases. Criteria of local homogeneity are given in terms on connections.
Compact symplectic four-dimensional manifolds not admitting polarizations
On frames defined by horizontal spaces
Comments On The Canonical Formalism Of Time-Dependent Higher Order Lagrangians.
The geometry of a closed form
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
Classification of symmetries for higher order Lagrangian systems.
Global dynamics of media with microstructure.
Classification of symmetries for higher order Lagrangian systems II: The non-autonomous case.
Solving non-holonomic Lagrangian dynamics in terms of almost product structures.
Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.
Non-holonomic mechanical systems in jet bundles.
In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.
Conservation laws and symmetry in economic growth models: a geometrical approach.
The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian function...
Almost product structures and Poisson reduction of presymplectic systems.
On the geometric prequantization of brackets.
En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.
Compact symplectic four solvmanifolds without polarizations
A global characterization of jet bundles of -velocities and covelocities
A remark on compact symplectic manifolds not admitting complex structures
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