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.
Geometric flows and Kaehler reduction / Arezzo, Claudio; A., Della Vedova; G., La Nave. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - 13:2(2015), pp. 497-525. [http://dx.doi.org/10.4310/JSG.2015.v13.n2.a8]
Geometric flows and Kaehler reduction
AREZZO, Claudio;
2015-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
