On a compact Kähler manifold, a Kähler metric ω is called generalized quasi-Einstein (GQE) if it satisfies the equation (Formula presented.) for some holomorphic vector field X, where (Formula presented.) denotes the harmonic representative of the Ricci form (Formula presented.). GQE metrics are one of the self-similar solutions of the modified Kähler–Ricci flow: (Formula presented.). In this paper, we propose a method of studying the modified Kähler–Ricci flow on special projective bundles, called admissible bundles, from the view point of symplectic geometry. As a result, we can reduce the modified Kähler–Ricci flow to a simple PDE with one space variable. Moreover, we study the limiting behavior of the solution in some special cases.
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