Affine bundles are affine spaces over modules

Abstract

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an alternate proof of the main result of [13], showing that the characterization of vector bundles by means of their Lie algebras of homogeneous differential operators also holds for vector bundles of rank 1 and over any base manifolds.

13 pages

References in corpus (3)

• AV-differential geometry: Euler-Lagrange equations
• Frame-independent mechanics:geometry on affine bundles
• On a Lie Algebraic Characterization of Vector Bundles

Cited by in corpus (1)

• On Gel'fand-Kolmogoroff type results