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Distribution (differential geometry)
About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.
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01 Jan 2017
TL;DR: In this paper, a non-holonomic manifold is defined, which is a manifold with a certain non-integrable smooth sub-bundle of the tangent bundle, also called a distribution.
Abstract: In this course we carefully define the notion of a non-holonomic manifold, which is a manifold with a certain non-integrable smooth sub-bundle of the tangent bundle, also called a distribution. We define such concepts as horizontal distributions, bracket generating condition for distributions, a sub-Riemannian structure, hypoelliptic and subelliptic operators and others. We connect the geometry of a manifold, defined by non-holonomic constraints, with properties of hypoelliptic operators on that manifold.