Osaka Journal of Mathematics

Invariant complex structures on tangent and cotangent Lie groups of dimension six

Rutwig Campoamor-Stursberg and Gabriela P. Ovando

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Abstract

This paper deals with left invariant complex structures on simply connected Lie groups, the Lie algebra of which is of the type $\mathrm{T}_{\pi} \mathfrak{h}=\mathfrak{h} \ltimes_{\pi} V$, where $\pi$ is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on $\mathrm{T}_{\pi} \mathfrak{h}$ for $\mathfrak{h}$ a three dimensional real Lie algebra. First it was proposed the study of complex structures $J$ satisfying the constraint $J\mathfrak{h} = V$. Whenever $\pi$ is the adjoint representation this kind of complex structures are associated to non-singular derivations of $\mathfrak{h}$. This fact allows different kinds of applications.

Article information

Source
Osaka J. Math., Volume 49, Number 2 (2012), 489-513.

Dates
First available in Project Euclid: 20 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1340197936

Mathematical Reviews number (MathSciNet)
MR2945759

Zentralblatt MATH identifier
1256.53024

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 22E25: Nilpotent and solvable Lie groups

Citation

Campoamor-Stursberg, Rutwig; Ovando, Gabriela P. Invariant complex structures on tangent and cotangent Lie groups of dimension six. Osaka J. Math. 49 (2012), no. 2, 489--513. https://projecteuclid.org/euclid.ojm/1340197936


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