The Kähler submanifolds between the ball bundles and the complex Euclidean space

In this paper, we provide a sufficient condition on the non-existence of the common Kähler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over Kähler manifolds. Then we get the non-existence theorems on several classes of ball bundles whose base spaces are Hermitian symmetric spaces or the complete Kähler-Einstein manifolds.