For certain compact complex Fano manifolds $M$ with reductive Lie algebras of
holomorphic vector fields, we determine the analytic subvariety of the second
cohomology group of $M$ consisting of Kähler classes whose
Bando-Calabi-Futaki character vanishes. Then a Kähler class contains
a Kähler metric of constant scalar curvature if and only if the
Kähler class is contained in the analytic subvariety. On examination
of the analytic subvariety, it is shown that $M$ admits infinitely many
nonhomothetic Kähler classes containing Kähler metrics of
constant scalar curvature but does not admit any Kähler-Einstein
metric.
@article{1245849446,
author = {Tsuboi, Kenji},
title = {On the existence of K\"ahler metrics of constant scalar curvature},
journal = {Tohoku Math. J. (2)},
volume = {61},
number = {1},
year = {2009},
pages = { 241-252},
language = {en},
url = {http://dml.mathdoc.fr/item/1245849446}
}
Tsuboi, Kenji. On the existence of Kähler metrics of constant scalar curvature. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp. 241-252. http://gdmltest.u-ga.fr/item/1245849446/