RENORMALIZED CHERN-GAUSS-BONNET FORMULA FOR COMPLETE KAHLER-EINSTEIN METRICS

被引：14
|
作者：
Marugame, Taiji [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan
来源：
AMERICAN JOURNAL OF MATHEMATICS | 2016年 / 138卷 / 04期
关键词：
CONVEX CR STRUCTURES; BURNS-EPSTEIN INVARIANT; MONGE-AMPERE EQUATION; PSEUDOCONVEX DOMAINS; SMALL BALLS; VOLUME RENORMALIZATION; ACHE; 4-MANIFOLDS; BERGMAN-KERNEL; MANIFOLDS; CURVATURE;
D O I：
10.1353/ajm.2016.0034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a renormalized Gauss-Bonnet formula for a strictly pseudoconvex manifold with a complete Kahler metric given by a globally defined potential function near the boundary. When the metric is asymptotically Einstein, the boundary contribution in the formula is explicitly written down in terms of the pseudo-hermitian geometry of the boundary and is shown to be a global CR invariant. The CR invariant generalizes the Burns-Epstein invariant on 3-dimensional CR manifolds.
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页码：1067 / 1094
页数：28
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