Related papers: An integrability criterion for a projective limit …

We prove a Frobenius theorem for Banach distributions on manifolds that are modelled over locally convex spaces. Moreover, we recall how Frobenius theorems can be applied to infinite-dimensional Lie groups and obtain, that given a Lie…

This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient…

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…

We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fr\'{e}chet bundles and the compatibility with the different morphisms. This kind of structure seems to be a convenient…

To give a criterion for the integrability of Banach-Lie triple systems, we follow the construction of the period group of a Lie algebra and define the period group of a Lie triple system as an analogous concept. We show that a Lie triple…

We investigate the integrability of Fr\'{e}chet tangent distributions on Fr\'{e}chet manifolds. We introduce the local well-posedness Condition W for split tangent subbundles, which reduces the local integrability problem to solving initial…

We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we…

Given a projective sequence of Banach bundles, each one provided with a of weak symplectic form, we look for conditions under which, the corresponding sequence of weak symplectic forms gives rise to weak symplectic form on the projective…

The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with seminegative curvature on a compact Kaehler manifold. There are in fact…

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…

In this paper, we establish the Frobenius Theorem and a Principle for Critical Point under the Constraint of $C^1$ Submanifold in Banach Spaces.

In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we…

We describe certain sufficient conditions for an infinitely divisible probability measure on a class of connected Lie groups to be embeddable in a continuous one-parameter convolution semigroup of probability measures. (Theorem 1.3). This…

We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of…

We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat…

It is known that the classical Frobenius theorem on conditions of integrability for distributions of planes can be extended to the case of complex holomorphic distributions. We show that an alternative criterion for integrability, namely,…

We present a formalisation of the existence and uniqueness theorems of integral curves of vector fields on Banach manifolds in the Lean theorem prover. First, we formalize properties of differential equations on Banach spaces (the…

The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces. Infinite dimensional manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class on…

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of…

We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…