Distributions and Integrability

Will J. Merry
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Will J. Merry: ETH Zürich, Departement Mathematik

Chapter Chapter 14 in Lectures on Differential Geometry I, 2026, pp 119-127 from Springer

Abstract: Abstract In this chapter we introduce distributions on manifolds and prove the local version of the famous Frobenius Theorem. The global version of this theorem—which will be proved next chapter—is the cornerstone of an area of differential geometry called foliation theory. In this book we will use the (global) Frobenius Theorem to prove the Lie Correspondence Theorem 11.11 and the Quotient Manifold Theorem 13.6 . In Volume II we will use the Frobenius Theorem to show that flat connections on vector bundles have trivial restricted holonomy groups (Volume II Theorem 6.8).

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-03733-6_14

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DOI: 10.1007/978-3-032-03733-6_14

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