Recent Topics in Differential and Analytic Geometry

Recent Topics in Differential and Analytic Geometry

Volume 18 in Advanced Studies in Pure Mathematics
1990, Pages 327-337
Recent Topics in Differential and Analytic Geometry

On Rotationally Symmetric Hamilton's Equation for Kähler-Einstein Metrics

https://doi.org/10.1016/B978-0-12-001018-9.50015-4Get rights and content

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This chapter focuses on rotationally symmetric Hamilton's equation for Kähler–Einstein metric. Any Riemannian metric g0 with positive Ricci curvature on a compact three-dimensional manifold is deformed to an Einstein metric along the equation

, where rt denotes the Ricci tensor of gt and
the mean value of the scalar curvature. The chapter explains how the solution of an equation converges to a Kähler–Einstein metric if it exists, even on a compact Kahler manifold with positive first Chern class.

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