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Journals / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 4

Submanifolds of Riemannian Product Manifolds

Mehmet ATÇEKEN
Pages
389–401
Publication Date
2022-11-03
DOI
—
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AI Summary & Key Takeaways

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

Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D\bot-geodesic.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold.
📊
Key Findings & Data:Fundamental properties of these type submanifolds such as the integrability of the distributions D, D\bot and mixed-geodesic property are studied.
💡
Conclusion & Impact:Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D\bot-geodesic.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian Product Manifold · Real Space Form · Locally Riemannian Product and Curvature-Invariant Submanifold

Abstract

In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D\bot and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D\bot-geodesic.

Özet

In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D\bot and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D\bot-geodesic.

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Cite This Article

ATÇEKEN, M. (2022). Submanifolds of Riemannian Product Manifolds. Turkish Journal of Mathematics, Cilt: 29 - Sayı: 4, 389–401. https://ajindex.com/articles/608730

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References (1)

  1. 1] Atc.eken. M., and Kele¸s. S., Two Theorems On Invariant Submanifolds of Riemannian Product Manifold. Indian J. Pure and Appl. Math., 34(7): 1035-1044, July 2003. [2] Chen, B.Y., Geometry of Submanifolds. Marcel Dekker Inc., New York, 1973. [3] Ximin. L., and Shao. F-M., Skew Semi-Invariant Submanifolds of a Locally Product Manifold. Portugalie Mathematica. Vol.56, Fasc.3, 1999, pp. 319-327. [4] Matsumoto, K., On Submanifolds of Locally Product Riemannian Manifolds. TRU Mathematics 18-2, pp. 145-157, 1982. [5] Senlin, X., and Yilong. N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), 2000, pp. 213-218. [6] Sahin. B., and Atc.eken. M., Semi-Invariant Submanifolds of Riemannian Product Manifold. Balkan Journal of Geometry and Its Applications. Vol. 8, No.1, 2003, pp. 91-100. [7] Rovenski.V., Foliations On Riemannian Manifolds and Submanifolds. Birkhauser, Bostan, 1997. [8] Yano. K., and Kon. M., Structures on Manifolds. World Scientific Publishing Co. Ltd, 1984.