11 problems

Fix a positive integer $n$. Let $(M,T^{1,0}M)$ be a closed strictly pseudoconvex CR manifold of dimension $2n+1$ admitting a pseudo-Einstein contact form. For each partition…

An odd-dimensional sphere is the standard sphere $S^{2n+1}$, and a parallelizable manifold is a manifold with trivial tangent bundle. A Sasakian-Einstein metric is a Sasakian metri…

Sasakian uniformization conjecture. Then $M$ is CR biholomorphic to the standard Heisenberg group $\mathbb{H}_{n}$.

Let $f$ be a ${\bf w}$-homogeneous polynomial defining a Calabi-Yau $3$-fold, and let the associated link have Sasakian Hodge number $h_S^{2,1}$, while the Calabi-Yau $3$-fold has…

Let $f,g$ be weighted homogeneous polynomials on $\mathbb{C}^n$ of the same degree $d$, with weight vectors ${\bf w}_f$ and ${\bf w}_g$. Two such polynomials are weakly R-equivalen…

Let an $n$-dimensional toric Gorenstein singularity be associated with a polytope $\Delta_{n-1}$, either reflexive or non-reflexive. Let $Y$ be the associated Sasaki–Einstein base…

An iterated $S^3$ join in the Gorenstein case is a smooth manifold of odd dimension. Existence conjecture. In the Gorenstein case, the iterated $S^3$ joins admit smooth Sasaki–Eins…

Let $M$ be a complete noncompact Sasakian $(2n+1)$-manifold with positive pseudohermitian bisectional curvature. Let $\mathbf{H}_n=\mathbb{C}^n\times\mathbb{R}$ be the standard…

Let $M$ be a complete noncompact Sasakian $(2n+1)$-manifold with nonnegative pseudohermitian bisectional curvature, and let $\mathcal{O}_p^{CR}(M)$ denote the ring of all CR-holomo…

Let $M$ be a compact Sasakian $7$-manifold with positive transverse scalar curvature, and let ${\bf E}\to M$ be a Sasakian $G$-bundle. Let $A$ be an irreducible selfdual contact in…

Let $(M,g)$ be a $3$-Sasakian $7$-manifold, with Sasakian structures satisfying the quaternionic relations … Let $\mathcal{M}^\ast$ be the moduli space under consideration. The tra…