= Radial Kähler metric with Euclidean volume in complex dimension two
{title2=$\varphi_a'(s)=\sqrt{s^2+a^2}/(2s)$}
For $s=|z_1|^2+|z_2|^2>0$ and $a>0$, a <geometric Kähler potential> with derivative $\varphi'(s)=\sqrt{s^2+a^2}/(2s)$ defines a <Kähler metric> on $\mathbb C^2\setminus\{0\}$. Its tangential and radial <eigenvalues> are $\sqrt{s^2+a^2}/(2s)$ and $s/(2\sqrt{s^2+a^2})$. Their product is $1/4$, giving the same <Riemannian volume form> as $\omega_0=(i/2)\sum dz_j\wedge d\bar z_j$, although the metric is different. This construction makes preservation of volume compatible with anisotropic stretching.
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