Yıl 2024,
Cilt: 17 Sayı: 1, 24 - 33, 23.04.2024
Ali Uçum
,
Kazım İlarslan
,
Çetin Camcı
Kaynakça
- [1] Dede, M., Ekici, C., Goemans,W. and Ünlütürk, Y.: Twisted surfaces with vanishing curvature in Galilean 3-space. Int. J. Geom. Methods Mod.Phys. 15, 1850001 (13 pages)(2018).
- [2] Duggal, K. L. and Jin, D. H.: Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific Publishing (2007).
- [3] Goemans,W. andWoestyne, I. Van de: Twisted surfaces in Euclidean and Minkowski 3-space, Pure and Applied Differential Geometry: J. Vander Veken, I. Van de Woestyne, L. Verstraelen and L. Vrancken (Editors), Shaker Verlag Aachen, Germany, 143-151 (2013).
- [4] Goemans, W. and Woestyne, I. Van de: Constant curvature twisted surfaces in Euclidean and Minkowski 3-space. In: Proceedings of theconference ”Riemannian Geometry and Applications to Engineering and Economics-RIGA”, Bucharest, Romania, 117-130 (2014).
- [5] Goemans, W. and Woestyne, I. Van de: Twisted surfaces with null rotation axis in Minkowski 3-space. Results. Math. 70, 81-93 (2016).
- [6] Goemans,W.: Flat double rotattional surfaces in Euclidean and Lorentz-Minkowski 4-space. Publications de L’Institut Mathematique, Nouvellesérie, tome 103(117), 61–68(2018).
- [7] Gray, A., Abbena, E., Salamon S. (eds.): Modern Differential Geometry of Curves and Surfaces with Mathematica. Chapman & Hall/CRC,Boca Raton (2006).
- [8] Grbovic, M., Nešovic, E. and Panti´c, A.: On the second kind twisted surfaces in Minkowski 3-space. Int. Electron. J. Geom. 8(2), 9–20(2015).
- [9] Inoguchi, J. and Lee, S.: Null curves in Minkowski 3-space Int. Electron. J. Geom. 1 (2),40-83(2008).
- [10] Kazan, A. and Karada˘ g, H.B.:Twisted surfaces in the Pseudo-Galilean space. New Trends Math. Sci. 5, 72–79 (2017).
- [11] Kuhnel, W.: Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, (1999).
- [12] Lopez, R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom. 7 (1),44-107 (2014).
- [13] Moore, C. L. E.: Surfaces of rotation in a space of four dimensions. Ann. of Math. 21(2), 81–93 (1919).
- [14] O’Neill, B.: Semi-Riemannian Geometry. Academic Press, London (1983).
- [15] Stanilov, G., and Slavova, G.: Classification of some twisted surfaces and power series of such surfaces. Comptes Rendus de l’Academie Bulgaredes Sciences, 59(6),593-600 (2006).
- [16] Walrave, J.: Curves and surfaces in Minkowski space, Doctoral thesis, K.U. Leuven, Faculty of Science, Leuven (1995).
Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$
Yıl 2024,
Cilt: 17 Sayı: 1, 24 - 33, 23.04.2024
Ali Uçum
,
Kazım İlarslan
,
Çetin Camcı
Öz
In this paper, we consider the twisted surfaces in semi-Euclidean 4-space with index 2.We classify the twisted surface with respect to their spine curve which are non-null or null curves. So, we study the geometric properties of these surfaces. Also we obtain the family of some special surfaces such as flat surfaces, marginally trapped surfaces.
Kaynakça
- [1] Dede, M., Ekici, C., Goemans,W. and Ünlütürk, Y.: Twisted surfaces with vanishing curvature in Galilean 3-space. Int. J. Geom. Methods Mod.Phys. 15, 1850001 (13 pages)(2018).
- [2] Duggal, K. L. and Jin, D. H.: Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific Publishing (2007).
- [3] Goemans,W. andWoestyne, I. Van de: Twisted surfaces in Euclidean and Minkowski 3-space, Pure and Applied Differential Geometry: J. Vander Veken, I. Van de Woestyne, L. Verstraelen and L. Vrancken (Editors), Shaker Verlag Aachen, Germany, 143-151 (2013).
- [4] Goemans, W. and Woestyne, I. Van de: Constant curvature twisted surfaces in Euclidean and Minkowski 3-space. In: Proceedings of theconference ”Riemannian Geometry and Applications to Engineering and Economics-RIGA”, Bucharest, Romania, 117-130 (2014).
- [5] Goemans, W. and Woestyne, I. Van de: Twisted surfaces with null rotation axis in Minkowski 3-space. Results. Math. 70, 81-93 (2016).
- [6] Goemans,W.: Flat double rotattional surfaces in Euclidean and Lorentz-Minkowski 4-space. Publications de L’Institut Mathematique, Nouvellesérie, tome 103(117), 61–68(2018).
- [7] Gray, A., Abbena, E., Salamon S. (eds.): Modern Differential Geometry of Curves and Surfaces with Mathematica. Chapman & Hall/CRC,Boca Raton (2006).
- [8] Grbovic, M., Nešovic, E. and Panti´c, A.: On the second kind twisted surfaces in Minkowski 3-space. Int. Electron. J. Geom. 8(2), 9–20(2015).
- [9] Inoguchi, J. and Lee, S.: Null curves in Minkowski 3-space Int. Electron. J. Geom. 1 (2),40-83(2008).
- [10] Kazan, A. and Karada˘ g, H.B.:Twisted surfaces in the Pseudo-Galilean space. New Trends Math. Sci. 5, 72–79 (2017).
- [11] Kuhnel, W.: Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, (1999).
- [12] Lopez, R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom. 7 (1),44-107 (2014).
- [13] Moore, C. L. E.: Surfaces of rotation in a space of four dimensions. Ann. of Math. 21(2), 81–93 (1919).
- [14] O’Neill, B.: Semi-Riemannian Geometry. Academic Press, London (1983).
- [15] Stanilov, G., and Slavova, G.: Classification of some twisted surfaces and power series of such surfaces. Comptes Rendus de l’Academie Bulgaredes Sciences, 59(6),593-600 (2006).
- [16] Walrave, J.: Curves and surfaces in Minkowski space, Doctoral thesis, K.U. Leuven, Faculty of Science, Leuven (1995).