Gromov–D’Ambra classification conjecture for rigid geometric structures

Let $M$ be a compact manifold with a rigid geometric structure $\omega$, and let $H$ be a sufficiently large transformation group. Gromov–D’Ambra conjecture. All triples $(H,M,\omega)$ are almost classifiable. This conjecture proposes a broad classification of compact manifolds with rigid geometric structures and large transformation groups; the source does not specify a precise meaning of “sufficiently large” or the status of the conjecture.