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Some New Characterizations of Parallel Factorable Surface in Riemannian Three Dimensional Heisenberg Group

Year 2018, CMES 2018, 31 - 36, 30.11.2018
https://doi.org/10.17714/gumusfenbil.440949

Abstract

In
this paper, we give some properties of parallel factorable surface which is
obtained by group operations in Riemannian three dimensional Heisenberg Group
H₃. Then, we obtain some characterizetions of parallel factorable surface
according to Levi- Civita connections of H₃
.

References

  • Calvaruso, G. and Van der Veken, J., 2010. Parallel Surfaces in Three Dimensional Lie Groups. Taiwanese Journal of Mathematics, 14 (1), 223-250.
  • Fukui, T. and Hasegawa, M., 2012. Singularities of Parallel Surfaces. Tohoku Mathematical Journal, 64 (3), 387-408.
  • Kızıltuğ, S. and Yaylı, Y., 2012. Timelike Curves on Timelike Parallel Surfaces in Minkowski 3-space E₁³. Mathematica Aeterna, 2 (8), 689 – 700.
  • Körpınar, T. and Turhan, E., 2012. Spacelike Biharmonic New Type B-Slant Helices According to Bishop Frame in the Lorentzian Heisenberg Group H³. General Mathematics Notes, 10 (2), 36-42.
  • Körpınar, T. and Turhan, E., 2013. Parallel Surfaces to Normal Ruled Surfaces of General Helices in the Sol Space Sol³. Boletim Sociedade Paranaense de. Matematica, 31 (2), 245-253.
  • Meng, H. and Liu, H., 2009. Factorable Surfaces in 3- Minkowski Space, Bulletin of the Korean Mathematical Society. 46 (2), 155-169.
  • Nacar, S., Kankal, M. and Hınıs M. A, 2018. Çok Değişkenli Uyarlanabilir Regresyon Eğrileri (ÇDURE) ile Günlük Akarsu Akımlarının Tahmini-Haldizen Deresi Örneği. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8 (1), 38-47.
  • Safiulina, E., 2001. Parallel and Semi- parallel Space-like Surfaces in Pseudo- Euclidean Spaces. Proc.Estonian Acad. Sci. Phys. Math., 50 (1),16-33.
  • Turhan, E. and Altay, G., 2010. Maximal and Minimal Surfaces of Factorable Surfaces in Heis₃. Int. J.Open Problems Compt. Math., 3 (2), 200- 212.
  • Unluturk, Y. and Ekici, C., 2003. On Parallel Surfaces of Timelike Ruled Weingarten Surfaces. Balkan Journal of Mathematics, 01, 72-91.
  • Yılmaz, S., 2010. Bishop spherical images of a spacelike curve in Minkowski 3-space. International Journal of the Physical Sciences, 5 (6), 898-905.
  • Yoon, D.W., 2008. Some properties of parallel surfaces in Euclidean 3-spaces. Honam Mathematical Journal, 30 (4), 637-644.
  • Yu, Y. and Liu, H., 2007. The factorable minimal surfaces. Proceedings of The Eleventh International Workshop on Diff. Geom., 11, 33-39.

Üç Boyutlu Riemannian Heisenberg Grubunda Paralel Faktorable Yüzeylerin Bazı Karakterizasyonları

Year 2018, CMES 2018, 31 - 36, 30.11.2018
https://doi.org/10.17714/gumusfenbil.440949

Abstract

Bu çalışmada üç boyutlu Riemannian Heisenberg grubunda grup işlemiyle
elde edilen paralel faktorable yüzeylerin bazı özellikleri verildi. Daha sonra
H₃ te
Levi- Civita konneksiyonlarına göre paralel faktorable yüzeylerin bazı
karakterizasyonları elde edildi.

References

  • Calvaruso, G. and Van der Veken, J., 2010. Parallel Surfaces in Three Dimensional Lie Groups. Taiwanese Journal of Mathematics, 14 (1), 223-250.
  • Fukui, T. and Hasegawa, M., 2012. Singularities of Parallel Surfaces. Tohoku Mathematical Journal, 64 (3), 387-408.
  • Kızıltuğ, S. and Yaylı, Y., 2012. Timelike Curves on Timelike Parallel Surfaces in Minkowski 3-space E₁³. Mathematica Aeterna, 2 (8), 689 – 700.
  • Körpınar, T. and Turhan, E., 2012. Spacelike Biharmonic New Type B-Slant Helices According to Bishop Frame in the Lorentzian Heisenberg Group H³. General Mathematics Notes, 10 (2), 36-42.
  • Körpınar, T. and Turhan, E., 2013. Parallel Surfaces to Normal Ruled Surfaces of General Helices in the Sol Space Sol³. Boletim Sociedade Paranaense de. Matematica, 31 (2), 245-253.
  • Meng, H. and Liu, H., 2009. Factorable Surfaces in 3- Minkowski Space, Bulletin of the Korean Mathematical Society. 46 (2), 155-169.
  • Nacar, S., Kankal, M. and Hınıs M. A, 2018. Çok Değişkenli Uyarlanabilir Regresyon Eğrileri (ÇDURE) ile Günlük Akarsu Akımlarının Tahmini-Haldizen Deresi Örneği. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8 (1), 38-47.
  • Safiulina, E., 2001. Parallel and Semi- parallel Space-like Surfaces in Pseudo- Euclidean Spaces. Proc.Estonian Acad. Sci. Phys. Math., 50 (1),16-33.
  • Turhan, E. and Altay, G., 2010. Maximal and Minimal Surfaces of Factorable Surfaces in Heis₃. Int. J.Open Problems Compt. Math., 3 (2), 200- 212.
  • Unluturk, Y. and Ekici, C., 2003. On Parallel Surfaces of Timelike Ruled Weingarten Surfaces. Balkan Journal of Mathematics, 01, 72-91.
  • Yılmaz, S., 2010. Bishop spherical images of a spacelike curve in Minkowski 3-space. International Journal of the Physical Sciences, 5 (6), 898-905.
  • Yoon, D.W., 2008. Some properties of parallel surfaces in Euclidean 3-spaces. Honam Mathematical Journal, 30 (4), 637-644.
  • Yu, Y. and Liu, H., 2007. The factorable minimal surfaces. Proceedings of The Eleventh International Workshop on Diff. Geom., 11, 33-39.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Gülden Altay Suroğlu 0000-0003-1976-3465

Publication Date November 30, 2018
Submission Date July 5, 2018
Acceptance Date November 30, 2018
Published in Issue Year 2018 CMES 2018

Cite

APA Altay Suroğlu, G. (2018). Üç Boyutlu Riemannian Heisenberg Grubunda Paralel Faktorable Yüzeylerin Bazı Karakterizasyonları. Gümüşhane Üniversitesi Fen Bilimleri Dergisi31-36. https://doi.org/10.17714/gumusfenbil.440949