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Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Volume: 15 Issue: 2

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

Mohammad Nazrul Islam Khan(Qassim University)0000-0002-9652-0355
Lovejoy Das(Kent state University)0000-0002-2709-5113
Pages
—
Publication Date
2023-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tangent bundle · connection · Gauss equation

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.

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Cite This Article

Khan, M. N. I., Das, L. (2023). On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. Turkish Journal of Mathematics and Computer Science, Volume: 15 Issue: 2. https://doi.org/10.47000/tjmcs.1355887

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