We establish general sufficient conditions for the exact and global regularity of the \(\bar{\partial }\) -Neumann problem on smooth bounded pseudoconvex domains in complex manifolds. We first generalize Straube’s criterion from \(\mathbb {C}^n\) to general complex manifolds by reformulating the condition using purely imaginary vector fields and a metric contraction operator. We also introduce a condition for regularity that relaxes the requirement for strictly plurisubharmonic functions in favor of a “weak form” of the basic estimate. As a primary application, we establish global and exact regularity for the \(\bar{\partial }\) -Neumann operator and its associated operators on smoothly bounded pseudoconvex domains in \(\mathbb {C}\mathbb {P}^n\) that admit a plurisubharmonic defining function. In this setting, the space of \(L^2\) harmonic (p, q)-forms is trivial. These results provide a unified framework for regularity that addresses the challenges posed by the lack of strictly plurisubharmonic exhaustion functions on general manifolds.
