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Dergiler / 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 Yıldırım
Sayfa
967–970
Yayın Tarihi
2018-12-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The Golden Ratio is fascinating topic that continually generated news ideas.
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Temel Bulgular & Veri:Precisely, we can say that an (1,1)-tensor field   P  on a m-dimensional Riemann manifold M , g   is a Golden structure if it satisfies the equation P 2 = P + Id ,  where Id  is identity map on   M .
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Sonuç & Katkı:Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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   P  on a m-dimensional Riemann manifold M , g   is a Golden structure if it satisfies the equation P 2 = P + Id ,  where Id  is identity map on   M . Furthermore, g P X , Y = g X , P Y , the Riemannian metric is called    P -compatible and M , g , P   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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Bu Makaleye Atıf Yap

Erdoğan, F. E., Yıldırım, 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://doi.org/10.2339/politeknik.389629

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Kaynakça (8)

  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).
  2. Crasmareanu, M. and Hretcanu, C. E. “Golden differansiyel geometry”. Chaos, Solitons & Fractals 38, (5): 1229-1238, (2008).
  3. Crasmareanu, M. and Hretcanu, C. E. “Applications of the Golden Ratio on Riemannian Manifolds”. Turkish J. Math. 33, (2): 179-191, (2009).
  4. Gezer, A., Cengiz, N. and Salimov, A., “On integrability of Golden Riemannian structures”. Turkish J. Math. 37: 693-703, (2013).
  5. 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).
  6. Sahin, B. and Akyol, M. A., “Golden maps between Golden Riemannian manifolds and constancy of certain maps”, Math. Commun. 19: 333-342, (2014).
  7. Yano, K. And Kon, M., “Structures on manifolds”, World Scientific, Singapuore, Series in pure mathematics, 3 (1984).
  8. Erdoğan, F. E. And Yıldırım C. "Semi-invariant submanifolds of Golden Riemannian manifolds" AIP Conference Proceedings, 1833, 020044, doi:10.1063/1.4981692, (2017).