Yıl: 2019 Cilt: 12 Sayı: 1 Sayfa Aralığı: 61 - 70 Metin Dili: İngilizce İndeks Tarihi: 03-04-2020

New results on helix surfaces in the Minkowski 3-space

Öz:
In this paper, we characterize and classify helix surfaces with principal direction relatived to aspace-like and light-like, constant direction in the Minkowski 3-space.
Anahtar Kelime:

Konular: Matematik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Cermelli, P. and Di Scala, A. J., Constant-angle surfaces in liquid crystals. Philosophical Magazine 87 (2007), no 12, 1871–1888.
  • [2] Chen, B.-Y., Pseudo-Riemannian Geometry, -Invariants and Applications, World Scientific, Hackensack, NJ, 2011.
  • [3] Di Scala, A. J. and Ruiz-Hernandez, G., Helix submanifolds of euclidean spaces. Monatsh Math. 157 (2009), 205–215.
  • [4] Dillen, F., Fastenakels, J. and Van der Veken, J., Surfaces in S2  R with a canonical principal direction. Ann. Global Anal. Geom. 35 (2009), no 4, 381–396.
  • [5] Dillen, F., Fastenakels, J., Van der Veken, J. and Vrancken, L., Constant angle surfaces in S2  R. Monaths Math. 152 (2007), 89–96.
  • [6] Dillen, F. and Munteanu, M. I., Constant angle surfaces in H2  R. Bull. Braz. Math. Soc., New Series 40(1) (2009), 85–97.
  • [7] Dillen, F., Munteanu, M. I. and Nistor, A. I., Canonical coordinates and principal directions for surfaces in H2  R. Taiwanese J. Math. 15 (5) (2011), 2265–2289.
  • [8] Kelleci, A., Ergüt, M. and Turgay, N. C., New Classification Results on Surfaces with a Canonical Principal Direction in the Minkowski 3-space. Filomat 31 (2017), 6023–6040
  • [9] Fu, Y. and Nistor, A. I., Constant Angle Property and Canonical Principal Directions for Surfaces in M2(c)  R1. Mediterr. J. Math. 10 (2013), 1035–1049.
  • [10] Fu, Y. and Wang, X., Classification of Timelike Constant Slope Surfaces in 3-dimensional Minkowski Space. Results in Mathematics 63 (2013), 1095-1108.
  • [11] Fu, Y. and Yang, D., On constant slope space-like surfaces in 3-dimensional Minkowski space. J. Math. Analysis Appl. 385 (2012), 208 - 220.
  • [12] Garnica, E., Palmas, O. and Ruiz-Hernandez, G., Hypersurfaces with a canonical principal direction. Differential Geom. Appl. 30 (2012), 382–391.
  • [13] Güler, F., ¸Saffak, G. and Kasap, E., Timelike Constant Angle Surfaces in Minkowski Space R31 . Int. J. Contemp. Math. Sciences 6 (2011), no 44, 2189–2200.
  • [14] Lopez, R. and Munteanu, M. I., Constant angle surfaces in Minkowski space. Bull. Belg. Math. Soc. Simon Stevin, 18 (2011), 271–286.
  • [15] Munteanu, M. I., From golden spirals to constant slope surfaces. J. Math. Phys. 51(7)(2010), 073507.
  • [16] Munteanu, M. I. and Nistor, A. I., A new approach on Constant Angle Surfaces in E3 . Turk J. Math. 33 (2009), 169–178.
  • [17] Munteanu, M. I. and Nistor, A. I., Complete classification of surfaces with a canonical principal direction in the Euclidean space E3. Cent. Eur. J. Math. 9(2) (2011), 378–389.
  • [18] Nistor, A. I., A note on spacelike surfaces in Minkowski 3-space. Filomat 27(5) (2013), 843–849.
  • [19] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, World Scientific, New York, 1983.
  • [20] Tojeiro, R., On a class of hypersurfaces in Sn  R and Hn  R. Bull. Braz. Math. Soc. (N. S.) 41 (2010), no. 2, 199–209.
  • [21] Yang, D., Fu, Y. and Li, L., Geometry of space-like generalized constant ratio surfaces in Minkowski 3-space. Front. Math. China 12 (2017), 459-480.
APA Kelleci A, Turgay N, Ergüt M (2019). New results on helix surfaces in the Minkowski 3-space. , 61 - 70.
Chicago Kelleci Alev,Turgay Nurettin Cenk,Ergüt Mahmut New results on helix surfaces in the Minkowski 3-space. (2019): 61 - 70.
MLA Kelleci Alev,Turgay Nurettin Cenk,Ergüt Mahmut New results on helix surfaces in the Minkowski 3-space. , 2019, ss.61 - 70.
AMA Kelleci A,Turgay N,Ergüt M New results on helix surfaces in the Minkowski 3-space. . 2019; 61 - 70.
Vancouver Kelleci A,Turgay N,Ergüt M New results on helix surfaces in the Minkowski 3-space. . 2019; 61 - 70.
IEEE Kelleci A,Turgay N,Ergüt M "New results on helix surfaces in the Minkowski 3-space." , ss.61 - 70, 2019.
ISNAD Kelleci, Alev vd. "New results on helix surfaces in the Minkowski 3-space". (2019), 61-70.
APA Kelleci A, Turgay N, Ergüt M (2019). New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry, 12(1), 61 - 70.
Chicago Kelleci Alev,Turgay Nurettin Cenk,Ergüt Mahmut New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry 12, no.1 (2019): 61 - 70.
MLA Kelleci Alev,Turgay Nurettin Cenk,Ergüt Mahmut New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry, vol.12, no.1, 2019, ss.61 - 70.
AMA Kelleci A,Turgay N,Ergüt M New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry. 2019; 12(1): 61 - 70.
Vancouver Kelleci A,Turgay N,Ergüt M New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry. 2019; 12(1): 61 - 70.
IEEE Kelleci A,Turgay N,Ergüt M "New results on helix surfaces in the Minkowski 3-space." International Electronic Journal of Geometry, 12, ss.61 - 70, 2019.
ISNAD Kelleci, Alev vd. "New results on helix surfaces in the Minkowski 3-space". International Electronic Journal of Geometry 12/1 (2019), 61-70.