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.
Symplectic and cosymplectic foliations on cosymplectic manifolds.
Examples of stable compact symplectic foliations on compact symplectic manifolds
Almost contact structures and time-dependent Lagrangians
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.
Examples of compact complex manifolds with no Kahler structure
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.
Page 1 Next