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Journals / Adıyaman Üniversitesi Eğitim Bilimleri Dergisi / 2012 / Cilt: 2 - Sayı: 2

On Biharmonic Curves in 3-dimensional Heisenberg Group

3-boyutlu Heisenberg Grubun Biharmonik Eğrileri Üzerine

Selcen Yüksel PERKTAŞ
Erol KILIÇ
Pages
58–74
Publication Date
2012-03-01
DOI
—
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AI Summary & Key Takeaways

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

We also show that there do not exist non-geodesic timelike horizontal biharmonic curves in 3-dimensional hyperbolic Heisenberg group with a semi-Riemannian metric of index 2.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group with a semi-Riemannian metric of index 2.
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Key Findings & Data:We prove that all of the non-geodesic non-null biharmonic curves in such a 3-dimensional hyperbolic Heisenberg group are helices.
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Conclusion & Impact:We also show that there do not exist non-geodesic timelike horizontal biharmonic curves in 3-dimensional hyperbolic Heisenberg group with a semi-Riemannian metric of index 2.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Biharmonik Eğriler · Yatay Eğriler · Heisenberg Grup.

Abstract

In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group with a semi-Riemannian metric of index 2. We prove that all of the non-geodesic non-null biharmonic curves in such a 3-dimensional hyperbolic Heisenberg group are helices. Moreover, we obtain explicit parametric equations for non-geodesic non-null biharmonic curves and non-geodesic spacelike horizontal biharmonic curves, respectively. We also show that there do not exist non-geodesic timelike horizontal biharmonic curves in 3-dimensional hyperbolic Heisenberg group with a semi-Riemannian metric of index 2.

Özet

Bu çalışmada indeksi 2 olan bir semi-Riemann metriğe sahip 3-boyutlu Heisenberg grubun jeodezik olmayan non-null biharmonik eğrileri çalışıldı. Bu şekildeki bir 3-boyutlu Heisenberg grubun jeodezik olmayan non-null biharmonik eğrilerinin helis olduğu ispatlandı. Ayrıca sırasıyla jeodezik olmayan non-null biharmonik eğriler ve jeodezik olmayan spacelike yatay biharmonik eğriler için açık parametrik denklemler elde edildi. İndeksi 2 olan bir semi-Riemann metriğe sahip 3-boyutlu Heisenberg grup üzerinde jeodezik olmayan timelike yatay biharmonik eğrilerin var olmadığı gösterildi.

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Cite This Article

PERKTAŞ, S. Y., KILIÇ, E. (2012). On Biharmonic Curves in 3-dimensional Heisenberg Group. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, Cilt: 2 - Sayı: 2, 58–74. https://ajindex.com/articles/450993

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References (21)

  1. A. Balmu, Sci. Ann. Univ. Agric. Sci. Vet. Med., 2004, 47, 87-96.
  2. R. Caddeo, S. Montaldo, P. Piu, Rend. Mat. App. L., 2001, 21, 143-157.
  3. R. Caddeo, S. Montaldo, C. Oniciuc, Int. J. Math., 2001, 12, 867-876.
  4. R. Caddeo, C. Oniciuc, P. Piu, Rend. Sem. Mat. Univ. Politec. Torino, 2004, 62, 265-278.
  5. B. Y. Chen, S. Ishikawa, Mem. Fac. Sci. Kyushu Univ. Ser. A, 1991, 45(2), 323-347.
  6. B. Y. Chen, Soochow J. Math., 1991, 17, 169-188.
  7. J. T. Cho, J. Inoguchi, J. E. Lee, Annali di Matematica, 2007, 186, 685-701.
  8. J. Eells, J. H. Sampson, Amer. J. Math., 1964, 86, 109-160.
  9. D. Fetcu, Beitrâge Algebra Geom., 2005, 46, 513-521.
  10. D. Fetcu, C. Oniciuc, Abh. Math. Sem. Univ. Hamburg., 2007, 77, 179-190.
  11. D. Fetcu, C. Oniciuc, Pac. J. Math., 2009, 240, 85-107.
  12. D. Fetcu, Annali di Matematica, 2010, 189, 591-603.
  13. J. Inoguchi, Int. J. Math. Sci., 2003, 21, 1365-1368.
  14. J. Inoguchi, Colloq. Math., 2004, 100, 163-179.
  15. G.Y. Jiang, Chinese Ann. Math. Ser. A, 1986, 7, 130-144.
  16. G. Y. Jiang, Chinese Ann. Math. Ser. A, 1986, 7, 389-402.
  17. T. Körpınar, E. Turhan, The Arabian Journal for Science and Engineering, 2010, 35, 79-85.
  18. E. Turhan, T. Körpınar, Demonstratio Mathematica, 2009, 42(2), 423-428.
  19. E. Turhan, T. Körpınar, Z. Naturforsch., 2010, 65a, 641-648.
  20. S. Montaldo, C. Oniciuc, Revista De La Union Mathematica Argentina, 2006, 47(2), 1-22.
  21. T. Sasahara, Publ. Math. Debrecen, 2005, 67, 285-303.