I have tried to find the three Killing vectors for the metric $$ds^2 = dr^2 + r^2d \theta^2$$ that is, the Euclidean metric of ##\mathbb{R}^2## written in polar coordinates. I found these to be(adsbygoogle = window.adsbygoogle || []).push({});

$$\bigg(\text{first}\bigg) \ \ \xi_r = \text{Cos} \theta \\

\xi_\theta = -\text{rSin} \theta \\

\bigg(\text{second}\bigg) \ \ \xi_r = \text{Sin} \theta \\

{\xi_\theta = \text{rCos} \theta} \\

\bigg(\text{third}\bigg) \ \ \xi_r = 0 \\

\xi_\theta = \text{r²}$$ As I have found solutions only for 3d on web, I would like to know whether these are correct or not.

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# I Killing's vectors

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