Hwang and Li introduced cone structures with characteristic conic connections, partially generalizing VMRT structures on uniruled projective manifolds. For isotrivial cone structures with fiber Z, they established a projective-geometric criterion on Z ensuring the existence of torsion-free connections on the associated G-structures.
In this talk, I will describe a classification of rational homogeneous varieties Z satisfying their criterion and its application to VMRT structures, generalizing results for adjoint varieties. I will explain how this problem naturally leads to the study of Gaussian maps.
