$SU(3)$ has dimension 8. Why is this not a complex manifold ?
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2026-05-05 18:46:47.1778006807
Way distinguishing whether or not complex manifold
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Because the unitary group is defined by non-complex-analytic equations (i.e., $AA^*=I$). Moreover, the only connected, compact complex submanifold of $\mathbb C^N$ is a point.