The Lie derivative of normal connections

In this paper, we state the Lie derivative of normal connection on a submanifold M of the Riemannian manifold M~. By this vein, we introduce the Lie derivative of the normal curvature tensor on M and give some relations between the normal curvature tensor on M and curvature tensor on M~ in the sense of the Lie derivative of normal connection. As an application, we give some detailed description of the normal curvature tensor on M whether M is a hypersubface.