Geodesic
Affine structures on jet and Weil bundles
David Blázquez-Sanz1
1 Escuela de Matemáticas Universidad Sergio Arboleda Calle 74, no. 14-14 Bogotá, Colombia
Colloquium Mathematicum, Tome 114 (2009) no. 2, pp. 291-305 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Weil algebra morphisms 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 passes to jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine structure on the groups of automorphisms of related Weil algebras.
DOI : 10.4064/cm114-2-10
Keywords: weil algebra morphisms induce natural transformations between weil bundles known cases natural transformation endowed canonical structure affine bundle structure arises only weil algebra morphism surjective its kernel has null square moreover cases structure affine bundle passes jet spaces characterization algebraic terms algebraic condition determines affine structure groups automorphisms related weil algebras

David Blázquez-Sanz 1

1 Escuela de Matemáticas Universidad Sergio Arboleda Calle 74, no. 14-14 Bogotá, Colombia 
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David Blázquez-Sanz. Affine structures on jet and Weil bundles. Colloquium Mathematicum, Tome 114 (2009) no. 2, pp. 291-305. doi: 10.4064/cm114-2-10

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