differential geometry w notes from teacher_Part_64

differential geometry w notes from teacher_Part_64 - 5.3...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5.3. FROBENIUS THEOREM 127 20. We define a transversal to F ( B ) ( n- k )-dimensional submanifold W with local coordinates y 1 , . . . , y n- k . 21. If the integral balls are su ffi ciently small, then for di ff erent points of W the integral balls at those points are disjoint. 5.3.3 Foliations • Let M be an n-dimensional manifold and Δ be a k-dimensional distribution on M . • Let Δ be in involution, and, therefore, integrable. • Then, at each point x of M there exists an integral manifold of Δ . • The integral manifold may return to the Frobenius coordinate patch around the point x infinitely many times. • Definition 5.3.5 The integral manifolds of an integrable distribution define a foliation of M. Each connected integral manifold is called a leaf of the foliation. A leaf that is not properly contained in another leaf is called a maximal leaf . • A maximal leaf is not necessarily an embedded submanifold....
View Full Document

This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.

Page1 / 2

differential geometry w notes from teacher_Part_64 - 5.3...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online