Affine Structures on Jet and Weil Bundles

Details Affine Structures on Jet and Weil Bundles Affine Structures on Jet and Weil Bundles

2009-01-28

arxiv.org/abs/0901.4483v1

David Bl\'azquez-Sanz, Affine Structures in Jet and Weil Bundles Colloq. Math. 114 (2009), no. 2, 291-305

Mathematics

Differential Geometry

16 pages

Scientific paper

Weil algebra morphism induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cases, this structure of affine bundle is passed down to Jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine structure between the groups of automorphisms of related Weil algebras

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