Holomorphic vector fields and characteristic forms on a Hermitian manifold (Q753163)

Let \(\Omega\) be the curvature form of the Hermitian connection of a compact Hermitian manifold M, with dim M\(=m\), and let F be a U(m)- invariant polynomial of degree \(k<m\). As F(\(\Omega\)) is a global closed 2k-form of M, it is called a characteristic form of M. The purpose of this paper is to calculate the integral \(\int_{M}F(\Omega)\wedge \sigma\), where \(\sigma\) is an arbitrary closed (2m-2k)-form of M. In the case when deg F\(=m\), this problem was solved by \textit{R. Bott} [J. Differ. Geom. 1, 311-330 (1967; Zbl 0179.288)].