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      Generalised subbundles and distributions: A comprehensive review

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          Abstract

          Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental part of mechanics and control theory. The theory of distributions is presented in a systematic way, and self-contained proofs are given of some of the major results. Parts of the theory are presented in the context of generalised subbundles of vector bundles. Special emphasis is placed on understanding the r\^ole of sheaves and understanding the distinctions between the smooth or finitely differentiable cases and the real analytic case. The Orbit Theorem and applications, including Frobenius's Theorem and theorems on the equivalence of families of vector fields, are considered in detail. Examples illustrate the phenomenon that can occur with generalised subbundles and distributions.

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          Journal
          19 September 2023
          Article
          2309.10471
          abb54c1e-fa2e-4dae-9a1d-70a5cb7978dc

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          58A30
          math.DG

          Geometry & Topology
          Geometry & Topology

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