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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 3

On the Geometry of Semi-Slant Submanifolds in Kenmotsu Manifolds endowed with the Schouten-van Kampen Connection

Semra Zeren(SIVAS SCIENCE AND TECHNOLOGY UNIVERSITY)0000-0003-0083-3507
Ahmet Yıldız(INONU UNIVERSITY)0000-0002-9799-1781
Pages
—
Publication Date
2026-10-13
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we provide a non-trivial example of a 5-dimensional semi-slant submanifold in ℝ⁷ to illustrate the theoretical results obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main objective of this paper is to investigate the geometry of semi-slant submanifolds in Kenmotsu manifolds defined with respect to the Schouten-van Kampen connection.
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Key Findings & Data:Unlike the Levi-Civita connection, the Schouten-van Kampen connection offers a more rigid geometric framework where the structure vector field ξ and the metric tensor remain parallel.
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Conclusion & Impact:Finally, we provide a non-trivial example of a 5-dimensional semi-slant submanifold in ℝ⁷ to illustrate the theoretical results obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Slant submanifolds · semi-slant submanifolds · Kenmotsu manifolds

Abstract

The main objective of this paper is to investigate the geometry of semi-slant submanifolds in Kenmotsu manifolds defined with respect to the Schouten-van Kampen connection. Unlike the Levi-Civita connection, the Schouten-van Kampen connection offers a more rigid geometric framework where the structure vector field ξ and the metric tensor remain parallel. In this study, we first establish the existence of semi-slant submanifolds in this setting and obtain necessary and sufficient conditions for their characterization. Furthermore, we investigate the integrability conditions of the invariant and slant distributions associated with the semi-slant structure. We derive new results concerning the total geodesicity of these submanifolds and the geometric properties of the induced connection. Finally, we provide a non-trivial example of a 5-dimensional semi-slant submanifold in ℝ⁷ to illustrate the theoretical results obtained.

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Cite This Article

Zeren, S., Yıldız, A. (2026). On the Geometry of Semi-Slant Submanifolds in Kenmotsu Manifolds endowed with the Schouten-van Kampen Connection. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 3. https://doi.org/10.47000/tjmcs.1880783

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