Complex, symplectic, and contact structures on low-dimensional lie groups

被引:0
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作者
Smolentsev N.K. [1 ]
机构
[1] Kemerovo State University, Kemerovo
关键词
Ahlerian Structure; Generalize Complex Structure; Invariant Complex Structure; Abelian Complex Structure;
D O I
10.1007/s10958-015-2385-6
中图分类号
学科分类号
摘要
It is well known that on any Lie group, a left-invariant Riemannian structure can be defined. For other left-invariant geometric structures, for example, complex, symplectic, or contact structures, there are difficult obstructions for their existence, which have still not been overcome, although a lot of works were devoted to them. In recent years, substantial progress in this direction has been made; in particular, classification theorems for low-dimensional groups have been obtained. This paper is a brief review of left-invariant complex, symplectic, pseudo-Kählerian, and contact structures on low-dimensional Lie groups and classification results for Lie groups of dimension 4, 5, and 6. © 2015 Springer Science+Business Media, Inc.
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页码:551 / 613
页数:62
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