Year: 2026
Type: preprint
Abstract: We classify the left-invariant complex structures on the real Lie group SL(2,C) up to Lie group automorphism. The classification consists of the bi-invariant complex structure, a family parameterised by the unit disk, and one new, non-regular complex structure. The topology of the space of left-invariant complex structures (modulo automorphisms) is not Hausdorff. Finally, we show that the corresponding complex manifolds always admit left-invariant balanced metrics.
Source: arXiv (Cornell University)
Authors: Kwong, Joseph, Mainenti, Asia
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170186757
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