Timeline for Hypersurfaces orthogonal to a cone
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2010 at 6:30 | comment | added | Michael Bächtold | Dear Dean, you are absolutely right, my argument invoking symplectic geometry wasn't needed. | |
| Sep 9, 2010 at 1:00 | comment | added | Deane Yang | If the codimension of $F$ is at least $1$, then there are additional integrability conditions that need to be satisfied. This can be analyzed using exterior differential systems. I suggest asking Robert Bryant; it is highly likely either Elie Cartan or he has analyzed this exact question before. | |
| Sep 8, 2010 at 20:57 | comment | added | Willie Wong | @Deane: for the time being, I am not requiring $F$ to be open. But you are right, if $F$ is open, as the parent assumed, then your method gives a very quick argument. | |
| Sep 8, 2010 at 18:27 | comment | added | Deane Yang | I don't see why symplectic geometry is needed if $F$ is open. Just fix any nonzero $\omega \in F_p \subset T_pM$. Choose any smooth function $f$ such that $df(p) = \omega$. Doesn't the distribution given by $df$ give you what you want? (The graph of $df$ is, of course, a Lagrangian submanifold, but you don't really need to know that) | |
| Sep 8, 2010 at 18:08 | comment | added | Willie Wong | Looks like I need to study a bit of symplectic geometry. I'd really appreciate it if you can take some time to elaborate later, but at the very least this should be enough of a clue to answer my original question. Thanks. | |
| Sep 8, 2010 at 17:59 | history | edited | Willie Wong | CC BY-SA 2.5 |
fixed display problems
|
| Sep 8, 2010 at 16:37 | comment | added | Michael Bächtold | sorry i don't know how to fix the output | |
| Sep 8, 2010 at 16:11 | history | answered | Michael Bächtold | CC BY-SA 2.5 |