The Lie derivative of normal connections
Bui Cao Van · The Journal of Nonlinear Sciences and Applications · 2016
In this paper, we state the Lie derivative of normal connection on a submanifold M of the Riemannian manifold \(\widetilde{M}\). 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 \(\widetilde{M}\) 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.