The Automorphism Group of a Banach Principal Bundle with {1}-structure

Details The Automorphism Group of a Banach Principal Bundle with {1}-structure The Automorphism Group of a Banach Principal Bundle with {1}-structure

2009-11-11

arxiv.org/abs/0911.2080v3

Geometriae Dedicata 154 (2011), 161-182

Mathematics

Differential Geometry

22 pages; minor corrections; reorganization of the proof of Prop. 3.1

Scientific paper

10.1007/s10711-010-9573-9

A {1}-structure on a Banach manifold M (with model space E) is an E-valued 1-form on M that induces on each tangent space an isomorphism onto E. Given a Banach principal bundle P with connected base space and a {1}-structure on P, we show that its automorphism group can be turned into a Banach-Lie group acting smoothly on P provided the Lie algebra of infinitesimal automorphisms consists of complete vector fields. As a consequence we show that the automorphism group of a connected geodesically complete affine Banach manifold M can be turned into a Banach-Lie group acting smoothly on M.

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