We investigate how to obtain various flows of Kãhler metrics on a fixed manifold as variations of Kãhler 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 Mabuchiâs metric, the Calabi flow, the pseudo-Calabi flow of Chen-Zheng and the Kãhler-Ricci flow. In the latter case we rederive the V-soliton equation of La Nave-Tian.
Arezzo, C., DELLA VEDOVA, A., La Nave, G. (2015). Geometric flows and Kähler reduction. JOURNAL OF SYMPLECTIC GEOMETRY, 13(2), 497-525 [10.4310/JSG.2015.v13.n2.a8].
Geometric flows and Kähler reduction
DELLA VEDOVA, ALBERTO
;
2015
Abstract
We investigate how to obtain various flows of Kãhler metrics on a fixed manifold as variations of Kãhler 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 Mabuchiâs metric, the Calabi flow, the pseudo-Calabi flow of Chen-Zheng and the Kãhler-Ricci flow. In the latter case we rederive the V-soliton equation of La Nave-Tian.
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