Mathematics – Differential Geometry
Scientific paper
2005-09-03
Trans. Amer. Math. Soc. 364 (2012), 3071-3135
Mathematics
Differential Geometry
Version 4 (64 pages): The two introductory sections have been completely rewritten. This includes an explicit reformulation of
Scientific paper
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and prolongation. We show how to construct certain normal forms (Cartan algebroids) for objects of finite-type, and are able to interpret these directly as infinitesimal symmetries deformed by curvature.' Details are developed for transitive structures but rudiments of the theory include intransitive structures (intransitive symmetry deformations). Detailed illustrations include subriemannian contact structures and conformal geometry.
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