Geometric structures as deformed infinitesimal symmetries

Details Geometric structures as deformed infinitesimal symmetries Geometric structures as deformed infinitesimal symmetries

2004-04-17

arxiv.org/abs/math/0404313v2

Trans. Amer. Math. 358 (2006), 3651-3671

Mathematics

Differential Geometry

Minor revision of first posting. Main changes: - "geometric structure" renamed "Cartan algebroid" - "geometric connection" ren

Scientific paper

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.

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