Invariant forms on complex manifolds with application to holomorphic mappings (Q788867)

Let \(\Omega\) be an n-dimensional complex manifold. The natural pairing \((\eta_ 1,\eta_ 2)=\int \eta_ 1\wedge {\bar \eta}_ 2\) is a biholomorphic invariant. In this paper it is used to discuss the representation of a cohomology class \(T\in H^ n(\Omega,{\mathbb{C}})\) by a unique holomorphic n-form \(\eta_ T\). Properties of \(\eta_ T\) are given, and it is shown that \(\eta_ T\) is smooth on \({\bar \Omega}\) if \(\partial \Omega\) is smooth and strongly pseudoconvex. - Application of the invariant n-form are given, including the explicit determination of Au\(t(\Omega)\) in special cases.