Journal of Symplectic Geometry

Volume 13 (2015)

Number 2

Geometric flows and Kähler reduction

Pages: 497 – 525



Claudio Arezzo (The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy)

Alberto Della Vedova (Dipartimento di Matematica, Università degli Studi di Parma, Italy)

Gabriele La Nave (Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, Il., U.S.A.)


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.

Published 13 April 2015