2021/11/25 by David Perrella, Perrella, David, David Pfefferlé +3
Mathematics · #58A30 (Primary) 53C12 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2111.12970
openalex publication_date 2021/11/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This paper completes the foundations of neatly integrable normal distribution\ntheory on manifolds with boundary. Normal distributions are those which contain\nvectors transverse to the boundary along its entirety. The theory is observed\nto be entirely analogous with the theory of integrable distributions on\nmanifolds due to Stefan and Sussmann. The main result is a one-to-one\ncorrespondence between so-called neatly integrable normal distributions and\nneat foliations by manifolds with boundary. Neat foliations are allowed to have\nnon-constant dimension and the leaves have boundary contained in the ambient\nboundary. The leaves satisfy a characteristic property formally identical to\nthat of weakly embedded submanifolds except in the category of manifolds with\nboundary.\n