  Let ${\mathcal B}_g(r)$ be the moduli space of triples of the form $(X,\,
K^{1/2}_X,\, F)$, where $X$ is a compact connected Riemann surface of genus
$g$, with $g\, \geq\, 2$, $K^{1/2}_X$ is a theta characteristic on $X$, and $F$
is a stable vector bundle on $X$ of rank $r$ and degree zero. We construct a
$T^*{\mathcal B}_g(r)$--torsor ${\mathcal H}_g(r)$ over ${\mathcal B}_g(r)$.
This generalizes on the one hand the torsor over the moduli space of stable
vector bundles of rank $r$, on a fixed Riemann surface $Y$, given by the moduli
space of holomorphic connections on the stable vector bundles of rank $r$ on
$Y$, and on the other hand the torsor over the moduli space of Riemann surfaces
given by the moduli space of Riemann surfaces with a projective structure. It
is shown that ${\mathcal H}_g(r)$ has a holomorphic symplectic structure
compatible with the $T^*{\mathcal B}_g(r)$--torsor structure. We also describe
${\mathcal H}_g(r)$ in terms of the second order matrix valued differential
operators. It is shown that ${\mathcal H}_g(r)$ is identified with the
$T^*{\mathcal B}_g(r)$--torsor given by the sheaf of holomorphic connections on
the theta line bundle over ${\mathcal B}_g(r)$.
