Geometric flows and Kähler reduction

We investigate how to obtain various flows of Kahler metrics on a fixed manifold as variations of Kahler reductions of a metric satisfying a given static equation on a higher dimensional manifold. We identify static equations that induce the geodesic equation for the Mabuchi's metric, the Calabi flow, the pseudo-Calabi flow of Chen-Zheng and the Kahler-Ricci flow. In the latter case we rederive the V-soliton equation of La Nave-Tian.