  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.
