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Year 2024, Volume: 17 Issue: 1, 24 - 33, 23.04.2024

Ali Uçum Kazım İlarslan Çetin Camcı

https://doi.org/10.36890/iejg.1404366

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).

Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$

Year 2024, Volume: 17 Issue: 1, 24 - 33, 23.04.2024

Ali Uçum Kazım İlarslan Çetin Camcı

https://doi.org/10.36890/iejg.1404366

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).
There are 16 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ali Uçum 0000-0003-0172-1531

Kazım İlarslan 0000-0003-1708-280X

Çetin Camcı 0000-0002-0122-559X

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

Cite

APA Uçum, A., İlarslan, K., & Camcı, Ç. (2024). Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$. International Electronic Journal of Geometry, 17(1), 24-33. https://doi.org/10.36890/iejg.1404366
AMA Uçum A, İlarslan K, Camcı Ç. Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$. Int. Electron. J. Geom. April 2024;17(1):24-33. doi:10.36890/iejg.1404366
Chicago Uçum, Ali, Kazım İlarslan, and Çetin Camcı. “Twisted Surfaces in Semi-Euclidean $4$-Space With Index $2$”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 24-33. https://doi.org/10.36890/iejg.1404366.
EndNote Uçum A, İlarslan K, Camcı Ç (April 1, 2024) Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$. International Electronic Journal of Geometry 17 1 24–33.
IEEE A. Uçum, K. İlarslan, and Ç. Camcı, “Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 24–33, 2024, doi: 10.36890/iejg.1404366.
ISNAD Uçum, Ali et al. “Twisted Surfaces in Semi-Euclidean $4$-Space With Index $2$”. International Electronic Journal of Geometry 17/1 (April 2024), 24-33. https://doi.org/10.36890/iejg.1404366.
JAMA Uçum A, İlarslan K, Camcı Ç. Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$. Int. Electron. J. Geom. 2024;17:24–33.
MLA Uçum, Ali et al. “Twisted Surfaces in Semi-Euclidean $4$-Space With Index $2$”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 24-33, doi:10.36890/iejg.1404366.
Vancouver Uçum A, İlarslan K, Camcı Ç. Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$. Int. Electron. J. Geom. 2024;17(1):24-33.
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