2 problems

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Gray–Wolf converse conjecture for homogeneous nearly Kähler manifolds
Gray–Wolf converse conjecture. Every homogeneous nearly Kähler manifold is a 3-symmetric space.
Conjecturesolved3-symmetric-spaces homogeneous-spaces nearly-kaehler-geometryarXiv posted 2 days ago
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Uniqueness conjecture for compact toric nearly Kähler manifolds
Toric nearly Kähler uniqueness conjecture. The only compact toric nearly Kähler manifold is $S^3\times S^3$ with its $3$ -symmetric nearly Kähler structure.
Conjectureopennearly-kaehler-geometry riemannian-geometry toric-geometryarXiv posted 2 days ago

Gray–Wolf converse conjecture for homogeneous nearly Kähler manifolds