Timeline for C^2 submanifolds contained in a hypersurface
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 6, 2013 at 17:32 | vote | accept | Dave Futer | ||
| Dec 6, 2013 at 15:50 | answer | added | Ricardo Andrade | timeline score: 9 | |
| Dec 5, 2013 at 17:21 | comment | added | Dave Futer | If the codimension is 1, there are really easy counterexamples (take a curve in $R^2$ which is $C^2$ but not smooth). If the codimension is 2, I'm not sure. In any case, codimension 3 is what naturally came up in a problem that a colleague of mine is studying. | |
| Dec 5, 2013 at 16:17 | comment | added | Willie Wong | Out of curiosity: Is there any particular reason why codimension at least 3? Are there known results for the case of lower codimension? | |
| Dec 5, 2013 at 13:06 | history | edited | Dave Futer | CC BY-SA 3.0 |
added 13 characters in body
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| Dec 5, 2013 at 13:05 | comment | added | Dave Futer | Yes, smooth is $C^\infty$, and I'm asking about regularity issues. | |
| Dec 5, 2013 at 8:58 | review | Close votes | |||
| Dec 5, 2013 at 10:18 | |||||
| Dec 5, 2013 at 8:45 | comment | added | Willie Wong | For immersed submanifolds: obviously not. For embedded submanifolds: use the constant rank theorem. Though maybe I am misunderstanding your question: is smooth $C^\infty$ here and are you asking about regularity issues? (If so, please edit to clarify, and in which case I retract my vote to close.) | |
| Dec 4, 2013 at 21:40 | history | asked | Dave Futer | CC BY-SA 3.0 |