Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 12 Sayı: 1, 61 - 70, 27.03.2019

Öz

Kaynakça

  • [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, δ-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 S^2 × 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 S^2 × R. Monaths Math. 152 (2007), 89–96.
  • [6] Dillen, F. and Munteanu, M. I., Constant angle surfaces in H^2 × 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 H^2 × 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 M^2(c) × R_1. 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.

New results on helix surfaces in the Minkowski 3-space

Yıl 2019, Cilt: 12 Sayı: 1, 61 - 70, 27.03.2019

Öz

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

Kaynakça

  • [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, δ-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 S^2 × 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 S^2 × R. Monaths Math. 152 (2007), 89–96.
  • [6] Dillen, F. and Munteanu, M. I., Constant angle surfaces in H^2 × 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 H^2 × 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 M^2(c) × R_1. 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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Alev Kelleci

Nurettin Cenk Turgay

Mahmut Ergüt Bu kişi benim

Yayımlanma Tarihi 27 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Kelleci, A., Turgay, N. C., & Ergüt, M. (2019). New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry, 12(1), 61-70.
AMA Kelleci A, Turgay NC, Ergüt M. New results on helix surfaces in the Minkowski 3-space. Int. Electron. J. Geom. Mart 2019;12(1):61-70.
Chicago Kelleci, Alev, Nurettin Cenk Turgay, ve Mahmut Ergüt. “New Results on Helix Surfaces in the Minkowski 3-Space”. International Electronic Journal of Geometry 12, sy. 1 (Mart 2019): 61-70.
EndNote Kelleci A, Turgay NC, Ergüt M (01 Mart 2019) New results on helix surfaces in the Minkowski 3-space. International Electronic Journal of Geometry 12 1 61–70.
IEEE A. Kelleci, N. C. Turgay, ve M. Ergüt, “New results on helix surfaces in the Minkowski 3-space”, Int. Electron. J. Geom., c. 12, sy. 1, 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 (Mart 2019), 61-70.
JAMA Kelleci A, Turgay NC, Ergüt M. New results on helix surfaces in the Minkowski 3-space. Int. Electron. J. Geom. 2019;12:61–70.
MLA Kelleci, Alev vd. “New Results on Helix Surfaces in the Minkowski 3-Space”. International Electronic Journal of Geometry, c. 12, sy. 1, 2019, ss. 61-70.
Vancouver Kelleci A, Turgay NC, Ergüt M. New results on helix surfaces in the Minkowski 3-space. Int. Electron. J. Geom. 2019;12(1):61-70.