In a series of works of Hwang and Mok, they verify the rigidity of rational homogeneous spaces of second Betti number one under Kaehler deformation. Inspired by these works, they conjecture that rational homogeneous spaces of second Betti number one can be characterized by their VMRT's (varieties of minimal rational tangents). The first part of this talk is on the verification of this conjecture, due to works of Hong, Hwang, Mok, Timashev and myself. Then we will turn to discuss the rigidity of rational homogeneous spaces of higher Betti numbers under Fano deformation.
