Timeline for A question about a one-form on Riemannian manifold
Current License: CC BY-SA 2.5
4 events
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| Aug 13, 2010 at 18:09 | comment | added | Otis Chodosh | Just modify José's answer a little bit. For example over $\mathbb{R}^2$ if we take standard coordinates $x^1,x^2$, then $\omega = dx^1$ and $X = f(x^1,x^2) \frac{\partial}{\partial x^1} + \frac{\partial}{\partial x^2}$. Then $\omega(X)\vert_{(x^1,x^2)} = f(x^1,x^2)$, and neither $\omega$ or $X$ is ever zero for any choice of $f$. Just choose $f$ with any sort of isolated zeroes you want. | |
| Aug 13, 2010 at 14:00 | comment | added | Chen | Thanks! I want to construct a $\omega$ with isolated nontivial zeros. But I don't known how to do it. | |
| Aug 13, 2010 at 10:58 | comment | added | damiano | Ehehe, we seem to have the same interpretation of the question! d | |
| Aug 13, 2010 at 10:57 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |