The aim of this work is to study the properties of the Lie derivative of currents and generalized forms on Riemann manifolds. For an application, we give some results of the Lie derivative of currents and generalized forms on Lie groups.

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.

The aim of this work is to study some properties of the Lie derivative and the exterior derivative connecting with the linear connection on the algebra. For an application, our interest for studying of the Lie derivative of differential forms on linear algebra from the ideas for using the Lie derivative of the linear connections. It will be useful in studying on the curvature tensor and the sorsion tensor.