EUDML

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

Marisa Fernández; Manuel de León — 1989

Commentationes Mathematicae Universitatis Carolinae

Comments On The Canonical Formalism Of Time-Dependent Higher Order Lagrangians.

Paulo R. Rodrigues; Manuel de Leon de — 1987

Revista colombiana de matematicas

Examples of compact complex manifolds with no Kahler structure

Cordero, Luis A.; Fernández, Marisa; León, Manuel de — 1987

Portugaliae mathematica

The geometry of a closed form

Marisa Fernández; Raúl Ibáñez; Manuel de León — 1998

Banach Center Publications

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 $G_{2}$ -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.

Classification of symmetries for higher order Lagrangian systems.

Manuel de León; David Martín de Diego — 1994

Extracta Mathematicae

Global dynamics of media with microstructure.

Ernst Binz; Manuel de León; Dan Socolescu — 1999

Extracta Mathematicae

Classification of symmetries for higher order Lagrangian systems II: The non-autonomous case.

Manuel de León; David Martín de Diego — 1994

Extracta Mathematicae

Solving non-holonomic Lagrangian dynamics in terms of almost product structures.

Manuel de León; David Martín de Diego — 1996

Extracta Mathematicae

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.

Manuel de León; David Martín de Diego — 1996

Extracta Mathematicae

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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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

On frames defined by horizontal spaces

Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies

Compact symplectic four-dimensional manifolds not admitting polarizations

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

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.

Non-holonomic mechanical systems in jet bundles.