Jan 20, 2017 · (It's not correct to say that an integral manifold is a "submanifold of the distribution," since the ...

You can find a discussion of a technique for finding integral manifolds based on the proof of the Frobenius theorem in pages 498-499 of Lee's "Introduction to Smooth Manifolds" book.

Jun 17, 2016 · The reason they are correct is precisely because the integral of a differential form does transform correctly, without its value changing, under a change of coordinates. Added: …

I'm trying to understand why the line of slope y passing through (x,y) is an integral manifold. My intuition tells me that there exists a point in the slope field where the distribution cannot be …

Jun 8, 2012 · I do not understand the following: "Let D be a smooth distribution on M such That through each point of M there passes an integral manifold of D". I understand the distribution …

Dec 6, 2018 · This is a good point to pause and think geometrically about what the integral submanifolds of these two vector fields might be. Using this observation, you should be able to …

Restricting the domain of an integral on a manifold. 3. Integrating the Riemannian volume form. 15.

Sep 28, 2020 · This integration by parts identity does not hold in general. The divergence theorem $$ \int_M\operatorname{div}(X)\mu_g=\int_{\partial M}g(N,X)\mu_{\iota^*g} $$ (Where …

Jan 4, 2021 · $\begingroup$ without orientation your result will be inconsistent: choosing a different, but compatible atlas, with random orientation in each chart then the integral will had …

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