On Bott–Chern forms and their applications

We use Chern–Weil theory for Hermitian holomorphic vector bundles with canonical connections for explicit computation of the Chern forms of trivial bundles with special non-diagonal Hermitian metrics. We prove that every (formula presented).The latter result is a complex manifold analogue of Proposition 2.6 in the paper by Simons and Sullivan (Am Math Soc 11:579–599, 2010). As an application, we obtain an explicit formula for the Bott–Chern form of a short exact sequence of holomorphic vector bundles considered by Bott and Chern (Acta Math 114:71–112, 1965), for the case when the first term is a line bundle.