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.

引用

页码：220 / 227

页数：8