Geodesics on a supermanifold and projective equivalence of superconnections

in Journal of Geometry & Physics (2013), 67

On a Lie Algebraic Characterization of Vector Bundles

in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2012)

We prove that a vector bundle E -> M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector ... [more ▼]

We prove that a vector bundle E -> M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole f ibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229{239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1. [less ▲]

Créer son document écrit avec LaTeX

Conference (2011, May 26)

LaTeX est un traitement de texte orienté contenu, gratuit et qui produit des documents de qualité typographique irréprochable. LaTeX nécessite un petit apprentissage, mais il s’agit d’un investissement ... [more ▼]

LaTeX est un traitement de texte orienté contenu, gratuit et qui produit des documents de qualité typographique irréprochable. LaTeX nécessite un petit apprentissage, mais il s’agit d’un investissement dont on récolte très vite les fruits. Le document présente le fonctionnement général de LaTeX, les notions de base nécessaires à la rédaction d'un premier document de type article et comment devenir autonome dans l’apprentissage. [less ▲]

Affine bundles are affine spaces

Poster (2010, September 13)

We show that the category of affine bundles over a smooth manifold M is equivalent to that of affine spaces modeled on locally free modules over the algebra of smooth functions on M.