Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature
Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature
复制标题
DOI：
10.2307/1971513
复制
发表时间：
1989-05
影响因子：
4.9
通讯作者：
N. Mok;J. Zhong
中科院分区：
文献类型：
--
作者：
N. Mok;J. Zhong
Siu-Yau [16] 研究了有限体积的完整凯勒流形和夹在两个负常数之间的黎曼截面曲率的紧致化。在[12]中，本文的第一作者开始系统地研究有限体积和有界曲率的完整 Kwhler 流形的紧致化更普遍的问题。提出了许多猜想，它们都可以被视为微分几何设置中算术簇紧化的猜想概括（即有界对称域 Q 与 Aut(Q) 的无挠算术子群的商）。从此以后，所有离散的自同构群都将被假定为无扭转的。在同一篇文章中，我们处理了 Kaihler 曲面的情况并证明：
Siu-Yau [16] studied the compactification of complete Kaihler manifolds of finite volume and of Riemannian sectional curvature pinched between two negative constants. In [12] the first author of the present article started a systematic study of the more general problem of compactifying complete Kwhler manifolds of finite volume and of bounded curvature. A number of conjectures were formulated, which can all be regarded as conjectural generalizations of the compactification of arithmetic varieties (i.e. quotients of bounded symmetric domains Q by torsion-free arithmetic subgroups of Aut(Q)) in a differentialgeometric setting. Here and henceforth all discrete groups of automorphisms will be assumed torsion-free. In the same article we treated the case of Kaihler surfaces and proved: