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MARC 21

Kähler-Einstein Metrics and Integral Invariants
Tag	Description
020	$a9783540391722$9978-3-540-39172-2
082	$a516.36$223
099	$aOnline resource: Springer
100	$aFutaki, Akito.
245	$aKähler-Einstein Metrics and Integral Invariants$h[EBook] /$cby Akito Futaki.
260	$aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bImprint: Springer,$c1988.
300	$aIV, 140 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aLecture Notes in Mathematics,$x0075-8434 ;$v1314
505	$aPreliminaries -- 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.
520	$aThese 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aLecture Notes in Mathematics,$x0075-8434 ;$v1314
856	$uhttp://dx.doi.org/10.1007/BFb0078084