Abstract. A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie algebroid structure. The curvature of this connection vanishes precisely when the structure is locally symmetric.This model generalizes Cartan geometries, a substantial class, to the intransitive case. Simple examples are surveyed and corresponding local obstructions to symmetry are identified. These examples include foliations, Riemannian structures, infinitesimal G-structures, symplectic and Poisson structures.

Abstract.Élie Cartan's general equivalence pr of Lie algebroids. The resulting formalism, bein allows for a full geometric interpretation of Carta reduction and prolongation. We show how to co (Cartan algebroids) for objects of finite-type, a directly as 'infinitesimal symmetries deformed b Details are developed for transitive structure include intransitive structures (intransitive symm illustrations include subriemannian contact stru try.c'est la dissymétrie qui crée le phénomène

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