ON THE EXISTENCE OF KAHLER METRICS OF CONSTANT SCALAR CURVATURE

摘要

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 Kahler classes whose Bando-Calabi-Futaki character vanishes. Then a Kahler class contains a Kahler metric of constant scalar curvature if and only if the Kahler class is contained in the analytic subvariety. On examination of the analytic subvariety, it is shown that M admits infinitely many nonhomothetic Kahler classes containing Kahler metrics of constant scalar curvature but does not admit any Kahler-Einstein metric.