Geometric structures as deformed infinitesimal symmetries
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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.References
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Additional Information
- Anthony D. Blaom
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- Received by editor(s): April 28, 2004
- Published electronically: March 24, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 3651-3671
- MSC (2000): Primary 53C15, 58H15; Secondary 53B15, 53C07, 53C05, 58H05
- DOI: https://doi.org/10.1090/S0002-9947-06-04057-8
- MathSciNet review: 2218993