Sp}(2)/{\rm Sp}(1)\times {\rm Sp}(1)\und
B_4={\rm Sp}(1,1)/{\rm Sp}(1)\times {\rm Sp}(1)$$ of positive and negative scalar curvature, respectively. Then one can consider Sp(2) fibred over $S^4$ and Sp(1,1) fibred over $B_4$ as principal bundles $$\label{4.3}
{\rm Sp}(2)\to S^4\und
{\rm Sp}(1,1)\to B_4\ ,$$ both with the structure group Sp(1)$\times$Sp(1).

Let us consider local sections of the fibrations (\[4.3\]) which are given by 4$\times$4 matrices $$\label{4.4}
Q:= f^{-\frac{1}{2}}\begin{pmatrix}{\bf 1}_2 &-\ve x\\x^\+ &
{\bf 1}_2\end{pmatrix}
\und
Q^{-1} = \eta Q^\+\eta =f^{-\frac{1}{2}}\begin{pmatrix}{\bf 1}_2 &\ve x\\
-x^\+ & {\bf 1}_2\end{pmatrix}\ ,$$ where $$\label{4.5}
x=x^\m\tau_\m\ ,\quad x^\+=x^\m\tau_\m^\+\ ,\quad
f:=1+\ve\,x^\+ x= 1+\ve\,r^2=1+\ve\de_{\m\n}x^\m x^\n\ ,$$ and matrices $$\label{4.6}
(\tau_\m )= (-\im\s_i, {\bf 1}_2)\und
(\tau_\m^\+ )= (\im\s_i, {\bf 1}_2)$$ obey $$\begin{aligned}
\nonumber
\tau_\m^\+ \tau_\n = \de_{\m\n}\cdot {\bf 1}_2 +
\eta_{\m\n}^i\,\im\,\s_i=:
\de_{\m\n}\cdot {\bf 1}_2 + \eta_{\m\n}\ ,\quad
\{\eta_{\m\n}^i\}=\{\ve^i_{jk}, \m{=}j, \n{=}k; \ \de_j^i,
\m{=}j, \n{=}4\}\ ,\\ \label{4.7}
\tau_\m\tau_\n^\+ = \de_{\m\n}\cdot {\bf 1}_2 + \bar\eta_{\m\n}^i\,
\im\,\s_i=: \de_{\m\n}\cdot {\bf 1}_2 + \bar\eta_{\m\n}\ ,\quad
\{\bar\eta_{\m\n}^i\}=\{\ve^i_{jk}, \m{=}j, \n{=}k; \ -\de_j^i,
\m{=}j, \n{=}4\}\ .\end{aligned}$$ Here $\{x^\m\}$ are local coordinates on ${{\cal U}}\subset S^4$ or $B_4$. Note that we will consistently combine formulae for both these spaces with the help of $\ve =\pm 1$. Matrices (\[4.4\]) are representative elements for cosets (\[4.2\]) encoding information about their differential geometry.

[**(Anti-)self-dual 