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Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Kähler-Einstein Metrics and Integral Invariants ([EBook] /) / by Akito Futaki.
Author	Futaki, Akito
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1988.
Physical Details	IV, 140 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1314
ISBN	9783540391722
Summary Note	These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be intrinsically defined on any compact complex manifold and becomes an obstruction to the existence of a Kähler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kähler-Einstein metric and lifting to a group character. Other related topics such as extremal Kähler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kählerian geometry and Chern-Simons theory are presented in full detail, these notes are accessible to graduate students as well as to specialists of the subject.:
Contents note	Preliminaries -- Kähler-Einstein metrics and extremal Kähler metrics -- The character f and its generalization to Kählerian invariants -- The character f as an obstruction -- The character f as a classical invariant -- Lifting f to a group character -- The character f as a moment map -- Aubin's approach and related results.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0078084
Links to Related Works	Subject References: Algebraic Geometry . Differential Geometry . Mathematics . Authors: Futaki, Akito . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 516.36 .

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Kähler-Einstein Metrics and Integral Invariants

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