Characterization of homogeneous varieties among Fano varieties
In this research, we study characterizations of highly symmetric rational homogeneous manifolds among Fano manifolds. The starting point of this research is the solution of the Hartshorne conjecture due to S. Mori: the only projective manifold with ample tangent bundle is the projective space. It is known that this conjecture is a generalization of the Frankel conjecture in complex geometry. After that, the generalized Frankel conjecture was solved by N. Mok. Based on this historical background, the final goal of our research is to solve the following conjecture due to F. Campana and T. Peternell, which is a generalization of the above conjectures including the Hartshorne conjecture: (CP conjecture) any Fano manifold with nef tangent bundle is rational homogeneous.