SPHERICAL PRODUCT SURFACES IN THE GALILEAN SPACE

Year 2016, Volume: 4 Issue: 2, 290 - 298, 01.10.2016

Muhittin Evren Aydın Alper Osman Ogrenmıs

Abstract

In the present paper, we consider the spherical product surfaces in a Galilean 3-space G3. We derive a classi cation result for such surfaces of constant curvature in G3. Moreover, we analyze some special curves on these surfaces in G3.

Keywords

Galilean plane, spherical product surface, Gaussian curvature, geo- desic line, asymptotic line

References

• [1] M. Akar, S. Yuce, N. Kuruoglu, One-parameter planar motion on the Galilean plane, Int. Electron. J. Geom. 6(2) (2013), 79-88.
• [2] K. Arslan, B. Kilic, Product submanifolds and their types, Far East J. Math. Sci. 6(1) (1998), 125-134.
• [3] M. E. Aydin, A. Mihai, A. O. Ogrenmis, M. Ergut, Geometry of the solutions of localized induction equation in the pseudo-Galilean space, Adv. Math. Phys., vol. 2015, Article ID 905978, 7 pages, 2015. doi:10.1155/2015/905978.
• [4] M. E. Aydin, I. Mihai, On certain surfaces in the isotropic 4-space, Math. Commun., in press.
• [5] A. H. Barr, Superquadrics and angle-preserving transformations, IEEE Comput.Graph. Appl. 1(1) (1981), 11-23.
• [6] B. Bulca, K. Arslan, B. (Kilic) Bayram, G. Ozturk, Spherical product surfaces in E4; An. St. Univ. Ovidius Constanta 20(1) (2012), 41{54.
• [7] B. Bulca, K. Arslan, B. (Kilic) Bayram, G. Ozturk, H. Ugail, On spherical product surfaces in E3, IEEE Computer Society, 2009, Int. Conference on CYBERWORLDS.
• [8] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18 (2013), 209{217.
• [9] M. Dede, C. Ekici, A. C. Coken, On the parallel surfaces in Galilean space, Hacettepe J. Math. Stat. 42(6) (2013), 605{615.
• [10] B. Divjak, Z.M. Sipus, Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces, Acta Math. Hungar. 98 (2003), 175{187.
• [11] M.P. do Carmo, Dierential Geometry of Curves and Surfaces, Prentice Hall: Englewood Clis, NJ, 1976.
• [12] Z. Erjavec, B. Divjak, D. Horvat, The general solutions of Frenet's system in the equiform geometry of the Galilean, pseudo-Galilean, simple isotropic and double isotropic space, Int. Math. Forum 6(17) (2011), 837 - 856.
• [13] Z. Erjavec, On generalization of helices in the Galilean and the pseudo-Galilean space, J. Math. Res. 6(3) (2014), 39-50.
• [14] A. Gray, Modern Dierential Geometry of Curves and Surfaces with Mathematica, CRC Press LLC, 1998.
• [15] I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean space G3; Rad Hazu Math. 456(10) (1991), 183-196.
• [16] M.K. Karacan, Y. Tuncer, Tubular surfaces of Weingarten types in Galilean and pseudo- Galilean, Bull. Math. Anal. Appl. 5(2) (2013), 87-100.
• [17] N. H. Kuiper, Minimal Total absolute curvature for immersions, Invent. Math., 10 (1970), 209-238.
• [18] A.O. Ogrenmis, M. Ergut, M. Bektas, On the helices in the Galilean Space G3; Iranian J. Sci. Tech., 31(A2) (2007), 177-181.
• [19] A. Onishchick, R. Sulanke, Projective and Cayley-Klein Geometries, Springer, 2006.
• [20] H. B. Oztekin, S. Tatlipinar, On some curves in Galilean plane and 3-dimensional Galilean space, J. Dyn. Syst. Geom. Theor. 10(2) (2012), 189-196.
• [21] B. J. Pavkovic, I. Kamenarovic, The equiform dierential geometry of curves in the Galilean space G3, Glasnik Mat. 22(42) (1987), 449-457.
• [22] Z.M. Sipus, Ruled Weingarten surfaces in the Galilean space, Period. Math. Hungar. 56 (2008), 213{225.
• [23] Z.M. Sipus, B.Divjak, Some special surface in the pseudo-Galilean Space, Acta Math. Hungar. 118 (2008), 209{226.
• [24] Z.M. Sipus, B. Divjak, Translation surface in the Galilean space, Glas. Mat. Ser. III 46(2) (2011), 455{469.
• [25] Z.M. Sipus, B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Sci., 2012, Art ID375264, 28pp.
• [26] D.W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glas. Mat. Ser. III, 48(2) (2013), 415-428.
• [27] D.W. Yoon, Some classication of translation surfaces in Galilean 3-space, Int. J. Math. Anal. 6(28) (2012), 1355-1361.
• [28] D. W. Yoon, Classication of rotational surfaces in pseudo-Galilean space, Glas. Mat. Ser. III 50(2) (2015), 453-465.