Fibrations on Banach manifolds

Olivia Gutú and Jesús A. Jaramillo

Vol. 215 (2004), No. 2, 313–329

DOI: 10.2140/pjm.2004.215.313

Abstract

Let f be a split submersion between paracompact Banach manifolds. We obtain here various conditions for f to be a fiber bundle. First, we give general conditions in terms of path-liftings. As a consequence, we deduce several criteria: For example, f is a fiber bundle provided it satisfies either some topological requirements (such as being a proper or a closed map) or, in the case of Finsler manifolds, some metric requirements (such as Hadamard integral condition).

Milestones

Received: 9 July 2003

Revised: 24 October 2003

Published: 1 June 2004