Geometric flows and K\"ahler reduction
Differential Geometry
2019-09-12 v1 Symplectic Geometry
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.
Cite
@article{arxiv.1304.5728,
title = {Geometric flows and K\"ahler reduction},
author = {Claudio Arezzo and Alberto Della Vedova and Gabriele La Nave},
journal= {arXiv preprint arXiv:1304.5728},
year = {2019}
}
Comments
18 pages