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arXiv · 2110.08533

Double sided torus actions and complex geometry on $SU(3)$

Hiroaki Ishida·Hisashi Kasuya
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Abstract

We construct explicit complex structures and transversely K\"ahler holomorphic foliations on $SU(3)$ corresponding to variations of real quadratic equations on a complex quadric in $\mathbb{C}^{6}$ as generalizations of left-invariant complex structures on $SU(3) $ and an invariant K\"ahler structure on the flag variety $SU(3)/T$.Consequently, we obtain orbifold variants of the flag variety $SU(3)/T$ as quotients of double sided torus actions.

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Hiroaki Ishida, Hisashi Kasuya. 2021-10-16. Double sided torus actions and complex geometry on $SU(3)$. https://arxiv.org/abs/2110.08533

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