Les idées de Louis Antoine concernant l'enseignement de la géométrie
Remarques sur les systèmes différentiels
On Liouville forms
We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.
Sur les structures presque complexes et autres structures infinitésimales régulières
Sur la géométrie des prolongements des espaces fibrés vectoriels
Cartan connections and momentum maps
Charles Ehresmann's concepts in differential geometry
We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.
Introduction to the theory of semi-holonomic jets
Lie algebroids and mechanics
We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold ; the set of units is the zero section identified with the manifold . We study the Legendre transformation on Lie algebroids.
Introduction to the theory of semi-holonomic jets.
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