On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection

Jing Li,Guoqing He,Peibiao Zhao

doi:10.3390/sym9070112

Jing Li, Guoqing He + Show 1 more

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https://doi.org/10.3390/sym9070112

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Journal: Symmetry	Publication Date: Jul 8, 2017
Citations: 6	License type: CC BY 4.0

Affiliation: Nanjing University of Science and Technology

Abstract

In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifolds with respect to the semi-symmetric non-metric connection.

Highlights

In 1924, Friedmann and Schouten [1] introduced the idea of semi-symmetric connection on b on a differentiable manifold M
Submanifolds of a Riemannian manifold with a semi-symmetric metric connection were studied by Nakao [4]
Motivated by [8] and [10], we have studied submanifolds of a Riemannian manifold endowed with the semi-symmetric non-metric connection defined by Equation (4) in this paper

Summary

Introduction

In 1924, Friedmann and Schouten [1] introduced the idea of semi-symmetric connection on b on a differentiable manifold M e is said to be a a differentiable manifold. Studied properties of submanifolds of a Riemannian manifold with this semi-symmetric non-metric connection. Motivated by [8] and [10], we have studied submanifolds of a Riemannian manifold endowed with the semi-symmetric non-metric connection defined by Equation (4) in this paper. 4, we deduce the Gauss, Codazzi, and Ricci equations with respect to the semi-symmetric non-metric connection.

Results

Conclusion