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