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Journals / Turkish Journal of Mathematics / 2001 / Cilt: 25 - Sayı: 3

On QR- submanifolds of a quaternionic space form

Bayram ŞAHİN
Pages
413–425
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that dim $upsilon^{perp}$ = 1 to be a 3-quasi Sasakian Manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:IIn this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition.
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Key Findings & Data:IIn this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition.
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Conclusion & Impact:Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that dim $upsilon^{perp}$ = 1 to be a 3-quasi Sasakian Manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

IIn this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that dim $upsilon^{perp}$ = 1 to be a 3-quasi Sasakian Manifold.

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Cite This Article

ŞAHİN, B. (2022). On QR- submanifolds of a quaternionic space form. Turkish Journal of Mathematics, Cilt: 25 - Sayı: 3, 413–425. https://ajindex.com/articles/608900

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References (1)

  1. 1] Bejancu, A.: QR-Submanifolds of Quaternion Kaehler manifolds, Chinese J.Math. Vol:14No:2 (1986). [2] Bejancu, A. Geometry of CR-Submanifolds, Kluwer,Dortrecht (1986) [3] Bejancu, A., Kon, M. & Yano, K.: CR-submanifolds of A Complex Space Form, J.Di.Geo.16, 137-145 (1981). [4] G ̈unes., R.,S.ahin, B. and Keles., S.: QR-Submanifolds and Almost Contact 3-Structure,Turkish J.Math. Vol:24 No:3,239-250 (2000) [5] Kuo, Y.Y.: On Almost Contact 3-Structure, Tohokou Math.J.22,325-332 (1970) [6] Sato, N.: Totally Real Submanifolds of a Complex Space Form with Non-Zero Parallel MeanCurvature Vector, Yokohoma Mat.J. 44 1-4(1997). [7] Yano, K. and Kon, M.: Structures on Manifolds, World Scienti c (1984)