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Smooth Schubert varieties in rational homogeneous manifolds of Picard number1 are horospherical varieties. We characterize standard embeddings of smoothSchubert varieties in rational homogeneous manifolds of Picard number 1 bymeans of varieties of minimal rational tangents. In particular, we mainlyconsider nonhomogeneous smooth Schubert varieties in symplectic Grassmanniansand in the 20-dimensional $F_4$-homogeneous manifold associated to a shortsimple root.

Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1