2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134472In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we obtain a definition of Chern-Simons classes of a (not necessarily flat) morphism between flat vector bundles on a smooth manifold. We extend Reznikov's theorem on triviality of these classes when the manifold is a compact Kähler manifold or a smooth complex quasi--projective variety, in degrees > 1.Algebraic GeometryMathematical Physics53C05, 53C07, 53C29text