$M^4$ and $B^{+}$ is a self-dual $su(2)$-connection on a rank-2 complex vector bundle over $M^4\cong{\mathbb C}P^2$ or ${\mathbb C}B_2$. Note that the field $B^{+}-b\cdot{\bf 1}_2$ can be identified with the $u(2)$-valued Levi-Civita connection on $M^4$ and then the curvature $F^{+}$ and $f^-\cdot{\bf 1}_2$ will be the self-dual ($su(2)$-valued) and anti-self-dual ($u(1)$-valued) parts of the Riemannian curvature tensor of the metric $\diff s^2=\th^1\th^{\1}+
\th^2\th^{\2}$ for $\th^{\a}$ given in (\[5.10\]).

[**Homogeneous twistor spaces of ${\mathbb C}P^2$ and ${\mathbb C}B_2$**]{}. Twistor spaces of ${\mathbb C}P^2$ and ${\mathbb C}B_2$ are the following nonsymmetric coset spaces: $$\label{5.15}
{{\cal T}}({\mathbb C}P^2) = {\rm SU(3)/U(1)}{\times}{\rm U(1)}\und
{{\cal T}}({\mathbb C}B_2) = {\rm SU(1,2)/U(1)}{\times}{\rm U(1)}\ .$$ They can be described via representative matrices similar to the twistor spaces ${{\cal T}}(S^4)$ and ${{\cal T}}(B_4)$ discussed before. Namely, we consider again the 2${\times}$2 matrix (\[4.20\]) and 3${\times}$3 matrices $$\label{5.16}
\hat G=\begin{pmatrix}1&0\\0&g\end{pmatrix}\und
\hat V=V\hat G\in\left\{\begin{array}{l}{\rm SU}(3)\quad {\rm for}\quad
\ve =1\\{\rm SU}(1,2)\quad {\rm for}\quad \ve =-1\end{array}\right.$$ for $V$ given in (\[5.4\]). The matrix $\hat V$ defines a local section of the bundle $$\label{5.17}
{\rm SU(3)}\to{{\cal T}}({\mathbb C}P^2)\qquad{\rm or}\qquad{\rm SU(1,2)}\to{{\cal T}}({\mathbb C}B_2)$$ depending on $\ve=\pm 1$. Both fibrations (\[5.17\]) have the group U(1)${\times}$U(1) as a typical fibre. Thus, the matrices (\[5.16\]) represent the twistor 