Abstract
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.
Keywords
Twisted surface normal curvature tensor parallel mean curvature vector minimal surface flat surface
References
- [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).
Abstract
References
- [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).
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | April 5, 2024 |
| Publication Date | April 23, 2024 |
| Submission Date | December 13, 2023 |
| Acceptance Date | April 1, 2024 |
| Published in Issue | Year 2024 Volume: 17 Issue: 1 |
