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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Existence of extremal metrics on compact almost homogeneous Kähler manifolds with two ends

Author: Daniel Guan
Journal: Trans. Amer. Math. Soc. 347 (1995), 2255-2262
MSC: Primary 58E11; Secondary 53C25, 53C55
MathSciNet review: 1285992
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Abstract: In this note we prove the existence and the uniqueness of extremal metrics in every Kähler class of any compact almost homogeneous Kähler manifold with two ends by considering the scalar curvature equations, those manifolds might not be projective. We also prove that there are extremal metrics in some Kähler classes of a completion of the multicanonical line bundle of a Kähler-Einstein manifold of positive Ricci curvature.

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Keywords: Extremal metrics, almost homogeneous manifolds, Kähler-Einstein manifolds, scalar curvature equations
Article copyright: © Copyright 1995 American Mathematical Society

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