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arXiv · 2607.20024

Invariant complex structures on SL(2,C)

Joseph Kwong·Asia Mainenti
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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.

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Joseph Kwong, Asia Mainenti. 2026-07-22. Invariant complex structures on SL(2,C). https://arxiv.org/abs/2607.20024

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