Geometric structures modeled after smooth projective horospherical varieties of Picard number one

Abstract

Geometric structures modeled after homogeneous manifolds are studied to characterize homogeneous manifolds and to prove the deformation rigidity of them. To generalize these characterizations and deformation rigidity results to quasihomogeneous manifolds, we first study horospherical varieties and geo metric structures modeled after horospherical varieties. Using Cartan geom etry, we prove that a geometric structure modeled after a smooth projective horospherical variety of Picard number one is locally equivalent to the stan dard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one.