Extremal Metrics On Ruled Manifolds
Differential Geometry
2013-10-14 v1 Algebraic Geometry
Abstract
In this paper, we consider a compact Kahler manifold with extremal Kahler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal Kahler metric is liftable to the bundle and if the bundle is relatively stable with respect to the action of automorphisms of the manifold, then there exist extremal Kahler metrics on the projectivization of the dual vector bundle.
Cite
@article{arxiv.1310.3006,
title = {Extremal Metrics On Ruled Manifolds},
author = {Zhiqin Lu and Reza Seyyedali},
journal= {arXiv preprint arXiv:1310.3006},
year = {2013}
}