Scholarlink

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).

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Distributions and Integrability

  • 章节

  • 发表日期：

    2026年

查看全文
  • Will J. Merry

摘要

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).