Examples of stable compact symplectic foliations on compact symplectic manifolds
Almost contact structures and time-dependent Lagrangians
Examples of compact complex manifolds with no Kahler structure
Higher order almost tangent geometry and non-autonomous Lagrangian dynamics
Tensor fields and connections on cross-sections in the frame bundle of second order of a parallelizable manifold.
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
Compact symplectic four-dimensional manifolds not admitting polarizations
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.
On frames defined by horizontal spaces
Symplectic and cosymplectic foliations on cosymplectic manifolds.
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.
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