The generalized Kähler Ricci flow

In this paper, we study a generalized Kähler Ricci flow, in which the Ricci term Ric is replaced by Ric−θ, where θθ is a closed real semi-positive (1, 1) form. We first introduce the generalized functionals WθWθ and μθμθ, and study their monotonicity along the generalized Kähler Ricci flow, then extend some of Perelman’s estimates to the generalized Kähler Ricci flow. We also study the asymptotic behavior of the generalized Ricci potential.