Timeline for Existence of a twice differentiable curve on a manifold
Current License: CC BY-SA 3.0
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| Mar 21, 2013 at 21:57 | comment | added | Misha | Note that both implicit function theorem and, hence, constant rank theorem, work without reduction in smoothness. Therefore, in OP's case, $S$ is locally a graph of a $C^2$-function and, hence, obviously contains $C^2$-curves tangent to every tangent vector. This (implicit function theorem) is undergraduate level material or 1-st year graduate material depending on the country. All in all, the question is not suitable for MO, math.stackexchange would be the right place. Voting to close. | |
| Mar 21, 2013 at 20:02 | comment | added | Ryan Budney | I think the OP suggested $H$ is just $C^2$. So the pre-image will only be $C^2$. | |
| Mar 21, 2013 at 19:55 | history | answered | Peter Michor | CC BY-SA 3.0 |