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arXiv · 0911.2080

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

Michael Klotz
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Abstract

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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Michael Klotz. 2009-11-11. The Automorphism Group of a Banach Principal Bundle with {1}-structure. https://doi.org/10.1007/s10711-010-9573-9

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