Journal of Symplectic Geometry
Volume 13 (2015)
Geometric flows and Kähler reduction
Pages: 497 – 525
We investigate how to obtain various flows of Kähler metrics on a fixed manifold as variations of Kähler 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 Kähler-Ricci flow. In the latter case we rederive the V-soliton equation of La Nave-Tian.