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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

5 votes
1 answer
148 views

Is $S$ a smooth submanifold of $M$?

Let $G$ be a Lie group and $H$ a Lie subgroup of $G$. Let $M$ be a smooth manifold. Let $\theta$ be a left smooth action of $G$ on $M$. Let $S=\{p\in M| G_p=H\}$, where $G_p$ is the isotropy gro …
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2 votes
1 answer
497 views

Is $H$ closed in $G$?

Every smooth manifold is assumed to be Hausdorff and second-countable. Suppose $G$ is a Lie group, $H$ is a Lie subgroup of $G$, $N$ is a closed Lie subgroup of $G$ such that $N$ is normal, $N\cap H= …
Born to be proud's user avatar