Affine connections and symmetry jets

Details Affine connections and symmetry jets Affine connections and symmetry jets

2011-03-11

arxiv.org/abs/1103.2300v1

Mathematics

Differential Geometry

68 pages, 8 figures

Scientific paper

We establish a bijective correspondence between affine connections and a class of jets of local diffeomorphisms of the underlying manifold called symmetry jets in the text. The symmetry jet corresponding to a torsionfree connection consists in the family of 2-jets of the geodesic symmetries. We then formulate, in terms of the symmetry jet, several aspects of the theory of affine connections and obtain geometric and intrinsic description of various related objects, like affine transformations, geodesics, horizontal distributions, affine extensions and curvature.

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