ИСТИНА

A key role in the geometry of Fano manifolds of Picard number one, which are sometimes called unipolar, is played by rational curves of minimal degree. Tangent directions of such curves through a general point form the so-called variety of minimal rational tangents (VMRT) in the projectivized tangent space. In 90-s J.-M. Hwang and N. Mok proposed a program of characterizing unipolar flag manifolds in the class of all unipolar Fano manifolds by their VMRT. Recently the program was successfully completed (J.-M. Hwang, Q. Li, and the speaker). The proof of the main result involves a bunch of ideas and techniques from "pure"algebraic geometry, differential geometry, structure and representation theory of simple Lie groups and algebras, and theory of spherical varieties.