List questions from manifolds

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In the Lie bracket $\mathcal L_X Y\equiv[X,Y]$ of vector fields, which integral curves are used?

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Published on 29 Apr 2026 - 5:47

List Question

Is $S$ a regular submanifold?

Compute the velocity vector.

Tangent space to a product

Simple exercise in cohomology

How can the proof of a local theorem on a manifold involving a map with a fixed point and a differential be reduced to the case of $\mathbb{R}^n$?

Orientability of projective space

About Sectional Curvature

Differential forms and how to show one is smooth

Problem about differential of a linear map

I have done the second direction of the proof. Hopefully, it is true. Please show my mistakes?

Lie bracket of vector fields on $\Bbb R^{n}$

projective cubic curve to complex projectie space

In the Lie bracket $\mathcal L_X Y\equiv[X,Y]$ of vector fields, which integral curves are used?

My question is about manifold related to submersion and immersion

Why is $\partial\partial M=\varnothing$?

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