Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

Murat Kemal Karacan; Dae Won Yoon; Nural Yuksel

doi:10.1515/awutm-2017-0006

.blurhash-client-img { display: none !important; }

Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 55 (2017): Issue 1 (July 2017)

By: Murat Kemal Karacan, Dae Won Yoon and Nural Yuksel

Open Access

|Sep 2017

Abstract

In this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I¹₃ under the condition ∆x_i= λ_ix_i where ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.

References

[1] M. E. Aydin, A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom, 107/3, (2016), 603-61510.1007/s00022-015-0292-0
Search in Google Scholar Back to article
[2] Z. Hanifi, M. Bekkar and Ch. Baba-Hamed, Translation surfaces in the threedimensional Lorentz-Minkowski Space satisfying firi = fiiri, Int. Journal of Math. Analysis, 4/17, (2010), 797 - 808
Search in Google Scholar Back to article
[3] C. Baikoussis and L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Sem. Math. Messina Ser. II, 2/16, (1993), 31-4210.3836/tjm/1270128488
Search in Google Scholar Back to article
[4] M. Bekkar, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying fixi = fiixi, Int. J. Contemp. Math. Sciences, 3/24, (2008), 1173-1185
Search in Google Scholar Back to article
[5] S. M. Choi, On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space, Tsukuba J. Math., 19/2, (1995), 351-36710.21099/tkbjm/1496162874
Search in Google Scholar Back to article
[6] F. Dillen, J. Pas and L. Verstraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica, 18, (1990), 239-246
Search in Google Scholar Back to article
[7] F. Dillen, J. Pas and L. Verstraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J., 13, (1990), 10-2110.2996/kmj/1138039155
Search in Google Scholar Back to article
[8] O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata, 34, (1990), 105-112 10.1007/BF00147319
Search in Google Scholar Back to article
[9] I. Kamenarovic, On natural geometry of ruled surfaces in isotropic space I1 3, Rad HAZU, Matematificke znanosti, 4, (1985), 45-60
Search in Google Scholar Back to article
[10] M. K. Karacan, D. W. Yoon and B. Bukcu, Translation surfaces in the three-dimensional simply isotropic space I1 3, Int. J. Geom. Methods Mod. Phys., 13 1650088, (2016), 9 pages10.1142/S0219887816500882
Search in Google Scholar Back to article
[11] H. Pottmann, P. Grohs and N. J. Mitra, Laguerre minimal surfaces, isotropic geometry and linear elasticity, Adv Comput Math, 31, (2009), 391-41910.1007/s10444-008-9076-5
Search in Google Scholar Back to article
[12] H. Sachs, Isotrope geometrie des raumes, Vieweg Verlag, Braunschweig, 199010.1007/978-3-322-83785-1
Search in Google Scholar Back to article
[13] B. Senoussi and M. Bekkar, Helicoidal surfaces with fir = Ar in 3-dimensional Euclidean space, Stud. Univ. Babes-Bolyai Math., 60/3, (2015), 437-448
Search in Google Scholar Back to article
[14] Z. M. Sipus, Translation surfaces of constant curvatures in a simply isotropic space, Period Math. Hung., 68, (2014), 160-17510.1007/s10998-014-0027-2
Search in Google Scholar Back to article
[15] Z. M. Sipus and B. Divjak, Mappings of ruled surfaces in simply isotropic space I1 3 that preserve the generators, Monatsh. Math., 139, (2003), 235-24510.1007/s00605-002-0526-8
Search in Google Scholar Back to article
[16] K. Strubecker, Difierentialgeometrie des isotropen Raumes III, Flachentheorie, Math. Zeitsch., 48, (1942), 369-42710.1007/BF01180022
Search in Google Scholar Back to article
[17] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18, (1966), 380-38510.2969/jmsj/01840380
Search in Google Scholar Back to article
[18] W. O. Vogel, Regelächen in isotropen raum, Journal für die reine und angewandte Mathematik, 202, (1959), 169-21410.1515/crll.1959.202.196
Search in Google Scholar Back to article
[19] D. W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glasnik Matematicki, 48/68, (2013), 415-42810.3336/gm.48.2.13
Search in Google Scholar Back to article
[20] D. W. Yoon, Some classification of translation surfaces in Galilean 3-Space, Int. Journal of Math. Analysis, 6/28, (2012), 1355-1361
Search in Google Scholar Back to article
[21] D. W. Yoon and J. W. Lee, Linear weingarten helicoidal surfaces in isotropic space, Symmetry, 8/11, (2016), 12610.3390/sym8110126
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/awutm-2017-0006 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

Journal RSS Feed

Language: English

Page range: 87 - 98

Submitted on: Oct 31, 2016

Accepted on: Mar 4, 2017

Published on: Sep 2, 2017

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Simply isotropic space,

Related subjects:

© 2017 Murat Kemal Karacan, Dae Won Yoon, Nural Yuksel, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 55 (2017): Issue 1 (July 2017)