On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection

Abstract

The object of this article is to study a quarter-symmetric non-metric connection in the tangent bundle and induced metric and connection on submanifold of co-dimension 2 and hypersurface concerning the quarter-symmetric non-metric connection in the tangent bundle. The Weingarten equations concerning the quarter-symmetric non-metric connection on a submanifold of co-dimension 2 and the hypersurface in the tangent bundle are obtained. Finally, authors deduce the Riemannian curvature tensor and Gauss and Codazzi equations on a submanifold of co-dimension 2 and hypersurface of the Riemannian manifold concerning the quarter-symmetric non-metric connection in the tangent bundle.

Keywords

• Tangent bundle
• connection
• Gauss equation
• mathematical operators
• Weingarten equation
• Codazzi equation
• partial differential equations
• curvature tensor
• submanifold

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