Journal of the Mathematical Society of Japan

Stability and existence of critical Kaehler metrics on ruled manifolds

Ying-Ji HONG

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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.

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

First available in Project Euclid: 24 March 2008

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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

constant scalar curvature Kaehler manifold momentum map stability automorphism group


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.

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