Timeline for How to show if $X$ is Killing field then it is tangent to the geodesic spheres centred at a point $p$?
Current License: CC BY-SA 4.0
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| Apr 5, 2019 at 19:55 | comment | added | James Dibble | The argument doesn't require that $p$ be the unique zero of $X$. It's easy to see that this isn't essential; for example, consider the Killing field $X$ obtained as the variational derivative of rotation around a line in $\mathbb{R}^3$. Every point along the line will be a zero of $X$, and each orbit circle is equidistant from each point on the line. | |
| Apr 5, 2019 at 5:33 | comment | added | Shreya | Also, do you mind telling where exactly uniqueness of point $p$ is being used? | |
| Apr 5, 2019 at 3:48 | comment | added | Shreya | I'm sorry but we haven't done first variation formula in class, it's a problem in do Carmo's chapter 3 while he introduces curvature and such not before chapter 4 so I believe we could do it without using that. | |
| Apr 5, 2019 at 0:53 | history | answered | James Dibble | CC BY-SA 4.0 |