Splitting submanifolds in rational homogeneous spaces of Picard number one

Let $M$ be a complex manifold. We prove that compact submanifold $S\subset M$ with splitting tangent sequence (called submanifold) is rational homogeneous when in large class of spaces Picard number one. Moreover, irreducible Hermitian symmetric, we $S$ must also symmetric. The basic tool use the restriction and projection map $\pi$ global holomorphic vector fields on ambient space which induced from condition. usage may help us set up new scheme to classify submanifolds explicit examples, as an example give differential geometric proof for classification $\dim\geq 2$ hyperquadric, has been previously proven using algebraic geometry.