On the existence of Kähler metrics of constant scalar curvature

2009/02/05 by Tsuboi, Kenji
#53C25 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0902.0861

Abstract

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.

Related

• Algebraic families of constant scalar curvature Kähler metrics
• Kähler-Einstein metrics along the smooth continuity method
• Kähler-Einstein metrics and Ding functional on \mathbb Q-Fano group compactifications
• The Space of Kaehler metrics
• Singular Kähler-Einstein metrics on \mathbb Q-Fano compactifications of Lie groups