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Journals / Politeknik Dergisi / 2018 / Cilt: 21 - Sayı: 4

On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

FEYZA ESRA ERDOĞAN
Cumali YILDIRIM
Pages
967–970
DOI
—
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AI Summary & Key Takeaways

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

Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Golden Ratio is fascinating topic that continually generated news ideas.
📊
Key Findings & Data:Precisely, we can say that an (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on .
💡
Conclusion & Impact:Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Semi-invariant submanifolds · Golden Riemannian manifolds · totally umbilical submanifolds

Abstract

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we can say that an (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on . Furthermore, , the Riemannian metric is called -compatible and is named a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. For this purpose, we study totally umbilical semi-invariant submanifold of the Golden Riemannian manifolds. Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.

Özet

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we can say that an (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on . Furthermore, , the Riemannian metric is called -compatible and is named a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. For this purpose, we study totally umbilical semi-invariant submanifold of the Golden Riemannian manifolds. Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.

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Cite This Article

ERDOĞAN, F. E., YILDIRIM, C. (2018). On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds. Politeknik Dergisi, Cilt: 21 - Sayı: 4, 967–970. https://ajindex.com/articles/306465

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References (9)

  1. Bejancu, A., “Geometry of CR-submanifolds”, D. Reidel, (1986)
  2. Chen, B.-Y. “Riemannian submanifolds, in Handbook of Differential Geometry”, North Holland (eds. F. Dillen and L. Verstraelen) I, 187418, (2000)
  3. Crasmareanu, M. and Hretcanu, C. E. “Golden differansiyel geometry”. Chaos, Solitons & Fractals 38, (5): 1229-1238, (2008)
  4. Crasmareanu, M. and Hretcanu, C. E. “Applications of the Golden Ratio on Riemannian Manifolds”. Turkish J. Math. 33, (2): 179-191, (2009)
  5. Gezer, A., Cengiz, N. and Salimov, A., “On integrability of Golden Riemannian structures”. Turkish J. Math. 37: 693-703, (2013)
  6. Hretcanu, C. E and Crasmareanu, M. “On some invariant submanifolds in a Riemannian manifold with golden structure”. An.Stiins. Univ. Al. I. Cuza Iasi. Mat. (N.S.)53, (1): 199-211, (2007)
  7. Sahin, B. and Akyol, M. A., “Golden maps between Golden Riemannian manifolds and constancy of certain maps”, Math. Commun. 19: 333-342, (2014)
  8. Yano, K. And Kon, M., “Structures on manifolds”, World Scientific, Singapuore, Series in pure mathematics, 3 (1984)
  9. Erdoğan, F. E. And Yıldırım C. "Semi-invariant submanifolds of Golden Riemannian manifolds" AIP Conference Proceedings, 1833, 020044, doi:10.1063/1.4981692, (2017).