The Lie derivative of normal connections

Abstract

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.

Design of continuous self‐calibration rotation scheme based on output sensitivity analysis

“…In this study, Lie-derivative is used to analyse the observability of the self-calibration model. Lie derivative is defined as [13]…”

Affine connections on the algebra of differential forms

“…We also gave some applications of our Gauss-Codazzi-Ricci equations. In [7], Van stated the Lie derivative of normal connection on a submanifold of the Riemannian manifold. He introduced the Lie derivative of the normal curvature tensor on the submanifold and gave some relations between the normal curvature tensor on the submanifold and curvature tensor on the ambient manifold in the sense of the Lie derivative of normal connection.…”