Locally conformally Kahler structures on unimodular Lie groups

被引：8

作者：

Andrada, A. ^{[1
]}

Origlia, M. ^{[1
]}

机构：

[1] Univ Nacl Cordoba, FaMAF CIEM, RA-5000 Cordoba, Argentina

来源：

GEOMETRIAE DEDICATA | 2015年 / 179卷 / 01期

关键词：

Hermitian metric; Locally conformally Kahler metric; Abelian complex structure; ABELIAN COMPLEX STRUCTURES; LEFT INVARIANT METRICS; NILMANIFOLDS; MANIFOLDS; GEOMETRY; SOLVMANIFOLDS; ALGEBRAS; EXAMPLES; TORSION;

D O I：

10.1007/s10711-015-0076-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study left-invariant locally conformally Kahler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is bi-invariant or abelian. In the former case, we show that no such Lie algebra is unimodular, while in the latter, we prove that if the Lie algebra is unimodular, then it is isomorphic to the product of and a Heisenberg Lie algebra.

引用

页码：197 / 216

页数：20

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