The geometry of weakly self-dual Kahler surfaces

被引：60

作者：

Apostolov, V

Calderbank, DMJ

Gauduchon, P

机构：

[1] Univ Quebec Montreal, Dept Math, Montreal, PQ H3C 3P8, Canada

[2] Univ Edinburgh, Dept Math & Stat, Edinburgh EH9 3JZ, Midlothian, Scotland

[3] Ecole Polytech, Ctr Math, CNRS, UMR 7640, F-91128 Palaiseau, France

来源：

COMPOSITIO MATHEMATICA | 2003年 / 135卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

almost-Kahler; 4-manifolds; Calabi extremal metrics; Kahler surfaces; weak self-duality;

D O I：

10.1023/A:1022251819334

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Kahler surfaces with harmonic anti-self-dual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including Kahler Einstein metrics and conformally Einstein Kahler metrics. We also extend some of our results to almost Kahler 4-manifolds, providing new examples of Ricci-flat almost Kahler metrics which are not Kahler.

引用

页码：279 / 322

页数：44

共 51 条

[1] Kahler geometry of toric varieties and extremal metrics [J].