In this article we discuss how the existence of Kaehler metrics with constant scalar curvature on the projectivization of a holomorphic vector bundle over a Kaehler manifold $M$ is related to a moment map condition for the action of the automorphism group of $M$ on the moduli of vector bundles.
@article{1206367963,
author = {HONG, Ying-Ji},
title = {Stability and existence of critical Kaehler metrics on ruled manifolds},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 265-290},
language = {en},
url = {http://dml.mathdoc.fr/item/1206367963}
}
HONG, Ying-Ji. Stability and existence of critical Kaehler metrics on ruled manifolds. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 265-290. http://gdmltest.u-ga.fr/item/1206367963/