Mathoverflow 1973

Does the 6-sphere $S^6$ admit the structure of a complex manifold?

Reference: mathoverflow/1973 asked by user Fetchinson0234

@[reducible, inline]

abbrev Mathoverflow1973.unitSphere (n : ℕ) : Set (EuclideanSpace ℝ (Fin (n + 1)))

The unit n-sphere, defined as Metric.sphere 0 1 in EuclideanSpace ℝ (Fin (n + 1)).

Equations

• Mathoverflow1973.unitSphere n = Metric.sphere 0 1

theorem Mathoverflow1973.mathoverflow_1973 : (∃ (atlas : ChartedSpace (EuclideanSpace ℂ (Fin 3)) ↑(unitSphere 6)), IsManifold (modelWithCornersSelf ℂ (EuclideanSpace ℂ (Fin 3))) 1 ↑(unitSphere 6)) ↔ sorry

Does the 6-sphere admit a complex structure, i.e. an atlas of holomorphically compatible charts relating it to EuclideanSpace ℂ (Fin 3)?