The Hermitian space-form conjecture

Let $M$ be a compact Hermitian manifold with Chern connection. Its holomorphic sectional curvature is the curvature of the Chern connection evaluated on complex lines in the holomorphic tangent bundle.

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 flat.

This conjecture is known in complex dimension $2$, but remains open in dimensions $3$ and higher in general. The paper confirms it for all solvmanifolds with complex commutator, extending earlier work on nilmanifolds.