Integrability of normal distributions Part 2: Neat foliations by manifolds with boundary
Abstract
This paper completes the foundations of neatly integrable normal distribution theory on manifolds with boundary. Normal distributions are those which contain vectors transverse to the boundary along its entirety. The theory is observed to be entirely analogous with the theory of integrable distributions on manifolds due to Stefan and Sussmann. The main result is a one-to-one correspondence between so-called neatly integrable normal distributions and neat foliations by manifolds with boundary. Neat foliations are allowed to have non-constant dimension and the leaves have boundary contained in the ambient boundary. The leaves satisfy a characteristic property formally identical to that of weakly embedded submanifolds except in the category of manifolds with boundary.
Keywords
Cite
@article{arxiv.2111.12970,
title = {Integrability of normal distributions Part 2: Neat foliations by manifolds with boundary},
author = {David Perrella and David Pfefferlé and Luchezar Stoyanov},
journal= {arXiv preprint arXiv:2111.12970},
year = {2021}
}
Comments
13 Pages, Part 2 of arXiv:2109.04845