Glasnik Matematicki, Vol. 50, No. 2 (2015), 441-451.

CLASSIFICATION OF FACTORABLE SURFACES IN THE PSEUDO-GALILEAN SPACE

Muhittin Evren Aydin, Alper Osman Öğrenmiş and Mahmut Ergüt

Department of Mathematics, Firat University, 23 200 Elazig, Turkey
e-mail: meaydin@firat.edu.tr

Department of Mathematics, Firat University, 23 200 Elazig, Turkey
e-mail: aogrenmis@firat.edu.tr

Department of Mathematics, Namik Kemal University, 59 000 Tekirdag, Turkey
e-mail: mergut@nku.edu.tr


Abstract.   In this paper, we introduce the factorable surfaces in the pseudo-Galilean space G31 and completely classify such surfaces with null Gaussian and mean curvature. Also, in a special case, we investigate the factorable surfaces which fulfill the condition that the ratio of the Gaussian curvature and the mean curvature is constant in G31.

2010 Mathematics Subject Classification.   53A35, 53B30.

Key words and phrases.   Factorable surface, Gaussian curvature, mean curvature, minimal surface, pseudo-Euclidean plane, pseudo-Galilean space.


Full text (PDF) (access from subscribing institutions only)

DOI: 10.3336/gm.50.2.12


References:

  1. M. E. Aydin and A. Mihai, Classifications of quasi-sum production functions with Allen determinants, Filomat 29(6) (2015), 1351-1359.

  2. M. Bekkar and B. Senoussi, Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying ∆ riiri, J. Geom. 103 (2012), 17-29.
    MathSciNet     CrossRef

  3. B. Divjak and Ž. M. Šipuš, Some special surfaces in the pseudo-Galilean space, Acta Math. Hungar. 118 (2008), 209-226.
    MathSciNet     CrossRef

  4. B. Divjak and Ž. M. Šipuš, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom. 77 (2003), 35-47.
    MathSciNet     CrossRef

  5. B. Divjak and Ž. M. Šipuš, Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces, Acta Math. Hungar. 98 (2003), 203-215.
    MathSciNet     CrossRef

  6. B.-Y. Chen, Geometry of submanifolds, M. Dekker, New York, 1973.
    MathSciNet    

  7. M. P. do Carmo, Differential geometry of curves and surfaces, Prentice Hall, Englewood Cliffs, NJ, 1976.
    MathSciNet    

  8. C. T. R. Conley, R. Etnyre, B. Gardener, L. H. Odom and B. D. Suceavă, New curvature inequalities for hypersurfaces in the Euclidean ambient space, Taiwanese J. Math. 17(3) (2013), 885-895.
    MathSciNet    

  9. M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18 (2013), 209-217.
    MathSciNet    

  10. I. Kamenarović, Existence theorems for ruled surfaces in the Galilean space G3, Rad Hrvatske Akad. Znan. Umjet. No. 456 (1991), 183-196.
    MathSciNet    

  11. M. K. Karacan and Y. Tuncer, Tubular surfaces of Weingarten types in Galilean and pseudo-Galilean, Bull. Math. Anal. Appl. 5 (2013), 87-100.
    MathSciNet    

  12. H. Meng and H. Liu, Factorable surfaces in 3-Minkowski space, Bull. Korean Math. Soc. 46 (2009), 155-169.
    MathSciNet     CrossRef

  13. Ž. Milin Šipuš, Ruled Weingarten surfaces in the Galilean space, Period. Math. Hungar. 56 (2008), 213-225.
    MathSciNet     CrossRef

  14. Ž. Milin Šipuš and B. Divjak, Translation surface in the Galilean space, Glas. Mat. Ser. III 46(66) (2011), 455-469.
    MathSciNet     CrossRef

  15. Ž. Milin Šipuš and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012, Art ID375264, 28pp.
    MathSciNet    

  16. A. O. Öğrenmiş, M. Ergüt and M. Bektaş, On the helices in the Galilean space G3, Iran. J. Sci. Technol. Trans. A Sci. 31 (2007), 177-181.
    MathSciNet    

  17. A. O. Öğrenmiş and M. Ergüt, On the Gauss map of ruled surfaces of type II in 3-dimensional pseudo-Galilean space, Bol. Soc. Parana. Mat. (3) 31 (2013), 145-152.
    MathSciNet     CrossRef

  18. E. Turhan, G. Altay, Maximal and minimal surfaces of factorable surfaces in Heis3, Int. J. Open Probl. Comput. Sci. Math. 3 (2010), 200-212.
    MathSciNet    

  19. G. E. Vilcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett. 24 (2011), 777-783.
    MathSciNet     CrossRef

  20. D. W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glas. Mat. Ser. III 48(68) (2013), 415-428.
    MathSciNet     CrossRef

  21. Y. Yu and H. Liu, The factorable minimal surfaces, in Proceedings of the Eleventh International Workshop on Differential Geometry, Kyungpook Nat. Univ., Taegu, 2007, 33-39.

Glasnik Matematicki Home Page