Tohoku Mathematical Journal

On the existence of Kähler metrics of constant scalar curvature

Kenji Tsuboi

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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.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 2 (2009), 241-252.

Dates
First available in Project Euclid: 24 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1245849446

Digital Object Identifier
doi:10.2748/tmj/1245849446

Mathematical Reviews number (MathSciNet)
MR2541408

Zentralblatt MATH identifier
1181.53061

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Keywords
Kähler manifold constant scalar curvature Bando-Calabi-Futaki character

Citation

Tsuboi, Kenji. On the existence of Kähler metrics of constant scalar curvature. Tohoku Math. J. (2) 61 (2009), no. 2, 241--252. doi:10.2748/tmj/1245849446. https://projecteuclid.org/euclid.tmj/1245849446


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