Integrability of weak distributions on Banach manifolds

TL;DR

This paper investigates the conditions under which weak distributions on Banach manifolds are integrable, extending previous results and applying to Banach Lie algebroids and Poisson manifolds.

Contribution

It introduces the concept of weak distributions on Banach manifolds and establishes new integrability conditions, generalizing prior work in the field.

Findings

Established conditions for integrability of weak distributions

Extended integrability theory to Banach Lie algebroids

Applied results to Banach Lie-Poisson manifolds

Abstract

This paper concerns the problem of integrability of non closed distributions on Banach manifolds. We introduce the notion of weak distribution and we look for conditions under which these distributions admit weak integral submanifolds. We give some applications to Banach Lie algebroid and Banach Lie-Poisson manifold. The main results of this paper generalize the works presented in [ChSt], [Nu] and [Gl].