Journal of the Mathematical Society of Japan

Stability and existence of critical Kaehler metrics on ruled manifolds

Ying-Ji HONG

Full-text: Open access

Abstract

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 information

Source
J. Math. Soc. Japan, Volume 60, Number 1 (2008), 265-290.

Dates
First available in Project Euclid: 24 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1206367963

Digital Object Identifier
doi:10.2969/jmsj/06010265

Mathematical Reviews number (MathSciNet)
MR2392011

Zentralblatt MATH identifier
1180.53039

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 58J37: Perturbations; asymptotics 32W50: Other partial differential equations of complex analysis 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 19B14: Stability for linear groups 53D20: Momentum maps; symplectic reduction

Keywords
constant scalar curvature Kaehler manifold momentum map stability automorphism group

Citation

HONG, Ying-Ji. Stability and existence of critical Kaehler metrics on ruled manifolds. J. Math. Soc. Japan 60 (2008), no. 1, 265--290. doi:10.2969/jmsj/06010265. https://projecteuclid.org/euclid.jmsj/1206367963


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References

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