$a$ is the one-monopole gauge potential (\[4.19\]) and $R$ is the radius of the Riemann sphere ${\mathbb C}P^1$ with the metric $$\label{4.23}
\diff s^2_{{\mathbb C}P^1}=\th^3\th^{\3}=
\frac{4R^2\diff\zeta\,\diff\bar\zeta}{(1+\zeta\bar\zeta)^2}\ .$$ The Kähler form on ${\mathbb C}P^1$ is $$\label{4.24}
\o_{{\mathbb C}P^1}=\sfrac{\im}{2}\,\th^3\wedge\th^{\3}\ .$$

Let us introduce 4$\times$4 matrices $$\label{4.25}
G=\begin{pmatrix}{\bf 1}_2&0\\0&g\end{pmatrix}\und\hat Q=QG\in
\left\{\begin{array}{l}{\rm Sp}(2)\subset{\rm SU}(4)
\quad {\rm for}\quad \ve =1\\
{\rm Sp}(1,1)\subset{\rm SU}(2,2)
\quad {\rm for}\quad \ve =-1\end{array}\right.$$ where $Q$ and $g$ are given in (\[4.4\]) and (\[4.20\]). The matrix $\hat Q$ is a local section of the bundle $$\label{4.26}
{\rm Sp}(2) \to {\rm Sp}(2)/{\rm Sp}(1){\times}{\rm U}(1)
=:{{\cal T}}(S^4)$$ or $$\label{4.27}
{\rm Sp}(1,1) \to {\rm Sp}(1,1)/{\rm Sp}(1){\times}{\rm U}(1)
=:{{\cal T}}(B_4)\ ,$$ depending on the choice $\ve =1$ or $\ve =-1$. In (\[4.26\]) and (\[4.27\]) the twistor spaces ${{\cal T}}(S^4)$ and ${{\cal T}}(B_4)$ appear as coset spaces and the matrices $\hat Q(\ve=\pm 1)$ from (\[4.25\]) are representatives for the cosets ${{\cal T}}(S^4)$ and ${{\cal T}}(B_4)$ which both are fibred, $$\label{4.28}
\pi :\quad {{\cal T}}(M^4) \to M^4\ ,$$ over $M^4=S^4$ or $B_4$ with ${\mathbb C}P^1=\,$SU(2)/U(1) as a typical fibre.

[**Kähler structure on twistor spaces ${{\cal T}}(S^4)$ and ${{\cal T}}(B_4)$**]{}. Let us consider a trivial complex vector bundle ${{\cal T}}(M^4){\times}{\mathbb C}^4$ with the flat connection $$\label{4.29}
\hat{{\cal A}}={\hat{Q}}^{-1}\diff{\hat{Q}}=G^{-1}{{\cal 