Year 2019,
Volume: 12 Issue: 1, 61 - 70, 27.03.2019
Alev Kelleci
,
Nurettin Cenk Turgay
,
Mahmut Ergüt
References
- [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
Year 2019,
Volume: 12 Issue: 1, 61 - 70, 27.03.2019
Alev Kelleci
,
Nurettin Cenk Turgay
,
Mahmut Ergüt
Abstract
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.
References
- [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.