4 problems

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The converse regularity conjecture for 3-Sasakian manifolds
Converse regularity conjecture. Every regular 3-Sasakian manifold is homogeneous.
Conjectureopen3-sasakian-geometry riemannian-geometryarXiv posted 2 days ago
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The positive quaternionic Kähler manifold conjecture
Regular $3$ -Sasakian manifolds arise as certain principal ${\rm SO}(3)$ or ${\rm Sp}(1)$ bundles over a quaternionic Kähler manifold with positive scalar curvature. An…
Conjectureopen3-sasakian-geometry quaternionic-kahler-geometry riemannian-geometryarXiv posted 2 days ago
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The homogeneity conjecture for regular 3-Sasakian manifolds
A regular $3$ -Sasakian manifold is a $3$ -Sasakian manifold whose associated Reeb foliation is regular. Homogeneity conjecture. Every regular $3$ -Sasakian manifold is homogeneous. T…
Conjectureopen3-sasakian-geometry homogeneous-manifolds riemannian-geometryarXiv posted 2 days ago
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Uniqueness conjecture for solutions of the qc Yamabe problem on the quaternionic sphere
On the unit $(4n+3)$ -dimensional sphere in quaternionic space, equip the sphere with its standard 3-Sasakian structure and consider the qc Yamabe problem in its conformal class. Th…
Conjectureopen3-sasakian-geometry qc-geometry yamabe-problemarXiv posted 2 days ago

The converse regularity conjecture for 3-Sasakian manifolds