The Lie derivative of normal connections

Volume 9, Issue 6, pp 4247--4256 http://dx.doi.org/10.22436/jnsa.009.06.66

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Authors

Bui Cao Van - Department of Mathematics, Vinh University, 182 Le Duan, Vinh City, Vietnam.

Abstract

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.

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Keywords

• Lie derivative
• normal connection
• normal curvature.

MSC

•  53C40
•  53C15
•  53C25

References

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