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).

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