  We establish general sufficient conditions for exact (and global) regularity
in the $\bar\partial$-Neumann problem on $(p,q)$-forms, $0 \leq p \leq n$ and
$1\leq q \leq n$, on a pseudoconvex domain $\Omega$ with smooth boundary
$b\Omega$ in an $n$-dimensional complex manifold $M$. Our hypotheses include
two assumptions: 1) $M$ admits a function that is strictly plurisubharmonic
acting on $(p_0,q_0)$-forms in a neighborhood of $b\Omega$ for some fixed $0
\leq p_0 \leq n$, $1 \leq q_0 \leq n$, or $M$ is a K\"ahler metric whose
holomorphic bisectional curvature acting $(p,q)$-forms is positive; and 2)
there exists a family of vector fields $T_\epsilon$ that are transverse to the
boundary $b\Omega$ and generate one forms, which when applied to $(p,q)$-forms,
$0 \leq p \leq n$ and $q_0 \leq q \leq n$, satisfy a "weak form" of the
compactness estimate.
  We also provide examples and applications of our main theorems.
