  In this article, we present characterizations of the concavity property of
minimal $L^2$ integrals degenerating to linearity in the case of fibrations
over products of open Riemann surfaces. As applications, we obtain
characterizations of the holding of equality in optimal jets $L^2$ extension
problem from fibers over products of analytic subsets to fibrations over
products of open Riemann surfaces, which implies characterizations of the
equality parts of Suita conjecture and extended Suita conjecture for fibrations
over products of open Riemann surfaces.
