Timeline for Is this a submanifold?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2019 at 18:45 | vote | accept | L.F. Cavenaghi | ||
| Mar 10, 2019 at 18:45 | comment | added | L.F. Cavenaghi | I will accept your answer since I could prove it was true following your comment, I will post the proof on the question. | |
| Mar 10, 2019 at 3:54 | history | edited | Steve Costenoble | CC BY-SA 4.0 |
added 470 characters in body
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| Mar 10, 2019 at 0:45 | comment | added | L.F. Cavenaghi | I have edited the question in order to encompass $S$ to it, it would be extremely helpful if you explain to me your thoughts on why $S$ has a chance to be a submanifold. | |
| Mar 10, 2019 at 0:37 | vote | accept | L.F. Cavenaghi | ||
| Mar 10, 2019 at 0:42 | |||||
| Mar 10, 2019 at 0:11 | comment | added | Steve Costenoble | My first reaction is that, yes, $S$ will be a submanifold. In fact, an open submanifold: If $p\in S$ then all points in an open neighborhood of $p$ should also satisfy your new condition. Essentially, a neighborhood of $p$ will look like $T_p M$ with the action of $G_p$. | |
| Mar 9, 2019 at 23:13 | comment | added | L.F. Cavenaghi | what if we change a little bit my definition by asking the following: $S = \{p \in M : \exists 0 \neq X \in \mathcal {H}_p \subset T_pM : G_X = G_p\}$? Now I ask if such $S$ is a submanifold of $M$, where $\cal H_p$ is the space $g$-orthogonal to $T_pG\cdot p$. | |
| Mar 9, 2019 at 23:01 | history | answered | Steve Costenoble | CC BY-SA 4.0 |