Volume 16, Issue 1 (4-2021)                   IJMSI 2021, 16(1): 123-135 | Back to browse issues page

XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Karacan M, Çakmak A, Kızıltuğ S, Es H. Surfaces Generated by Translation Surfaces of Type 1 in I^1_3. IJMSI. 2021; 16 (1) :123-135
URL: http://ijmsi.ir/article-1-1256-en.html
Abstract:  
In this paper, we classify surface at a constant distance from the edge of regression on translation surfaces of Type 1 in the three dimensional simply isotropic space I^1_3 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.
Type of Study: Research paper | Subject: Special

References
1. M.E.Aydin, A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom. 107 (3), (2016), 603-615. [DOI:10.1007/s00022-015-0292-0]
2. Ch. Baba-Hamed, M. Bekkar and H. Zoubir, Translation surfaces in the three dimensional Lorentz-Minkowski space satisfying ri = Ari, Int. Journal of Math. Analysis 4(17), (2010), 797-808.
3. M.Bekkar, B. Senoussi, Translation surfaces in the 3-dimensional space satisfying III ri = iri; J. Geom., 103, (2012), 367-374. [DOI:10.1007/s00022-012-0136-0]
4. B.Bukcu, D.W.Yoon and M.K.Karacan, Translation surfaces in the 3-dimensional simply isotropic space I^1_3 satisfying IIIxi = ixi, Konuralp Journal of Mathematics 4(1),(2016), 275-281.
5. A.Cakmak, O.Tarakci, Surfaces at a constant distance from the Edge of Regression on a Surface of Revolution in E3, Applied Mathematical Sciences, 10(15), (2016), 707-719. [DOI:10.12988/ams.2016.53222]
6. A. Cakmak, O. Tarakci, The image curves on surfaces at a constant distance from the edge of regression on a surface of revolution, International Journal of Mathematics and Computation, 1, (2016), 74-85. [DOI:10.1063/1.4945859]
7. B.Y. Chen, A report on submanifold of nite type, Soochow J. Math., 22, (1996), 117-337.
8. F. Dillen, J. Pas and L. Vertraelen, On surfaces of nite type in Euclidean 3-space, Kodai Math. J., 13, (1990), 10-21. [DOI:10.2996/kmj/1138039155]
9. F. Dillen, J. Pas and L. Vertraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica 18, (1990), 239-246.
10. O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata, 34, (1990), 105-112. [DOI:10.1007/BF00147319]
11. G. Kaimakamis, B. Papantoniou, K. Petoumenos, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying III r = Ar, Bull.Greek Math. Soc. 50, (2005), 75-90.
12. M.K.Karacan, D.W.Yoon and B.Bukcu, Translation surfaces in the three dimensional simply isotropic space I^1_3, Int. J. Geom. Methods Mod. Phys., 13, (2016), 1650088. [DOI:10.1142/S0219887816500882]
13. H. Sachs, Isotrope geometrie des raumes, Vieweg Verlag, Braunschweig, 1990. [DOI:10.1007/978-3-322-83785-1]
14. D. Saglam, O. B. Kalkan, Surfaces at a constant distance from the edge of regression on a surface in E3, Di erential Geometry-Dynamical Systems, 12, (2010), 187-200.
15. B.Senoussi, M. Bekkar, Helicoidal surfaces with J r = Ar in 3-dimensional Euclidean space, Stud. Univ. Babes-Bolyai Math. 60(13), (2015), 437-448.
16. Z.M. Sipus, Translation Surfaces of constant curvatures in a simply Isotropic space, Period Math. Hung. 68 (2014), 160-175. [DOI:10.1007/s10998-014-0027-2]
17. K. Strubecker, Di erentialgeometrie des Isotropen raumes III, Flachentheorie, Math. Zeitsch. 48, (1942), 369-427. [DOI:10.1007/BF01180022]
18. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. [DOI:10.2969/jmsj/01840380]
19. O. Tarakc , H.H Hac salihoglu, Surfaces at a constant distance from the edge of regression on a surface, Appl. Mathematics and Computation, 155, (2004), 81-93. [DOI:10.1016/S0096-3003(03)00761-6]
20. D.W.Yoon, On the Gauss map of translation surfaces in Minkowski 3-space, Taiwanese Journal of Mathematics, 6(3), (2002), 389-398. [DOI:10.11650/twjm/1500558304]
21. D.W.Yoon, Some classi cation of translation surfaces in Galilean 3-Space, Int. Journal of Math. Analysis, 6(28), (2012), 1355 - 1361.
22. S. Yurttancikmaz, O. Tarakci, The relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface, Advances in Mathematical Phys., (2015), Article ID 397126, 1-6. [DOI:10.1155/2015/397126]

Add your comments about this article : Your username or Email:
CAPTCHA

© 2021 CC BY-NC 4.0 | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb