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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...
The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane curve, which...
Une structure unimodulaire est définie sur une variété différentiable par une forme élément de volume. Différentes algèbres de Lie de dimension infinie attachées à une variété unimodulaire sont introduites et leurs idéaux étudiés. Ces idéaux sont semi-simples et de dimension infinie ; aucun idéal non trivial n’admet un idéal supplémentaire. Les dérivations de ces algèbres de Lie sont données par l’algèbre des champs de vecteurs reproduisant la forme de structure à un facteur constant près.
By using an invariant related to free Lie algebras, we give a criterion of non existence of isomorphism for the Pfaffian systems.
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