The flexible affine variety conjecture for RR-spaces

A smooth flexible complex affine variety is a smooth affine variety over the complex numbers whose algebraic automorphism group is generated by one-parameter unipotent subgroups. An $RR$-space is a complex manifold satisfying the Rosay–Rudin-space axioms described in the paper.

Flexible affine variety conjecture. Every smooth flexible complex affine variety is an $RR$-space.

This would extend the class of known $RR$-spaces beyond complex Euclidean spaces, character-free complex linear algebraic groups, and Danielewski surfaces. The paper indicates Proposition~ as a first step toward this conjecture; its general case remains open.