A new geometric flow over Kahler manifolds

摘要

In this paper, we introduce a geometric flow for Kahler metrics omega(t) coupled with closed (1, 1)-forms alpha(t) on a compact Kahler manifold, whose stationary solution is a constant scalar curvature Kahler (cscK) metric, coupled with a harmonic (1, 1)-form. We establish the long-time existence, i.e., assuming the initial (1, 1)-form alpha is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.