Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606212 | Differential Geometry and its Applications | 2012 | 11 Pages |
Abstract
We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that such a Hermitian structure is Kähler if and only if the Lie group is the direct product of several copies of the real hyperbolic plane by a Euclidean factor. Moreover, we show that if a left invariant Hermitian metric on a Lie group with an abelian complex structure has flat first canonical connection, then the Lie group is abelian.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A. Andrada, M.L. Barberis, I.G. Dotti,