We investigate how to obtain various flows of K"ahler metrics on a fixed manifold as variations of K"ahler 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 K"ahler-Ricci flow. In the latter case we re-derive the V-soliton equation of La Nave-Tian.
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