5 problems

Solvmanifold deformation conjecture. (i) Every left-invariant complex structure on $G$ is Stein, respectively biholomorphic to ${\bf C}^n$ in the nilpotent case. (ii) Every small d…

Hermitian space-form conjecture. If the Chern connection of $M$ has constant holomorphic sectional curvature, then $M$ must be either Kähler, hence a complex space form, or Chern f…

Let $M$ be a compact completely solvable manifold, and let $\omega$ be a symplectic structure on $M$. The Hard Lefschetz invariance conjecture. If $\omega$ satisfies the Hard Lefsc…

An expanding homogeneous Ricci soliton is a homogeneous Ricci soliton with soliton constant $\lambda<0$. A solvmanifold is a homogeneous space associated with a solvable Lie group;…

Let $M^3$ be the closed $3$-dimensional solvmanifold described in the source, let $\pi=\pi_1M^3$, and let $\mathcal P$ be the bounding class of polynomial functions. Let $E\pi$ be…