Journal of Differential Geometry

Gauge-Fixing Constant Scalar Curvature Equations on Ruled Manifolds and the Futaki Invariants

Ying-Ji Hong

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Abstract

In this article we introduce and prove the solvability of the gauge-fixing constant scalar curvature equations on ruled Kaehler manifolds. We prove that when some lifting conditions for holomorphic vector fields on the base manifold are satisfied the solutions for the gauge-fixing constant scalar curvature equations are actually solutions for the constant scalar curvature equations provided the corresponding Futaki invariants vanish.

Article information

Source
J. Differential Geom., Volume 60, Number 3 (2002), 389-453.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351123

Digital Object Identifier
doi:10.4310/jdg/1090351123

Mathematical Reviews number (MathSciNet)
MR1950172

Citation

Hong, Ying-Ji. Gauge-Fixing Constant Scalar Curvature Equations on Ruled Manifolds and the Futaki Invariants. J. Differential Geom. 60 (2002), no. 3, 389--453. doi:10.4310/jdg/1090351123. https://projecteuclid.org/euclid.jdg/1090351123


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