Small deformations and non-left-invariant complex structures on six-dimensional compact solvmanifolds

被引：12
|
作者：
Hasegawa, Keizo [1 ]
机构：
[1] Niigata Univ, Fac Educ, Dept Math, Nishi Ku, Niigata 9502181, Japan
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2010年 / 28卷 / 02期
关键词：
Solvmanifolds; Left-invariant complex structures; Pseudo-Kahler structures; KAHLER STRUCTURES; LIE-GROUPS; MANIFOLDS;
D O I：
10.1016/j.difgeo.2009.10.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a Continuous family of non-left-invariant complex structures. We also provide a complete classification of three-dimensional compact homogeneous complex solvmanifolds; and determine which of them admit pseudo-Kahler structures. (C) 2009 Elsevier B.V. All rights reserved.
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页码：220 / 227
页数：8
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