Glasnik Matematicki, Vol. 48, No. 2 (2013), 415-428.

SURFACES OF REVOLUTION IN THE THREE DIMENSIONAL PSEUDO-GALILEAN SPACE

Dae Won Yoon

Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, South Korea
e-mail: dwyoon@gnu.ac.kr

Abstract.   In the present paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space G31 . Also, we characterize surfaces of revolution in G31 in terms of the position vector field and Gauss map.

2010 Mathematics Subject Classification.   53A35, 53B30.

Key words and phrases.   Pseudo-Galilean space, surface of revolution, Gauss map.

Full text (PDF) (free access)

DOI: 10.3336/gm.48.2.13

References:

  1. L. J. Alías, A. Ferrández and P. Lucas, Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying Δ x = A x + B, Pacific J. Math. 156 (1992), 201-208.
    MathSciNet     CrossRef

  2. L. J. Alías, A. Ferrández, P. Lucas and M. A. Meroño, On the Gauss map of B-scrolls, Tsukuba J. Math. 22 (1998), 371-377.
    MathSciNet    

  3. C. Baikoussis and D. E. Blair, On the Gauss map of ruled surfaces, Glasgow Math. J. 34 (1992), 355-359.
    MathSciNet     CrossRef

  4. C. Baikoussis and L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Sem. Math. Messina Ser. II 2(16) (1993), 31-42.
    MathSciNet    

  5. C. Baikoussis and L. Verstraelen, The Chen-type of the spiral surfaces, Results Math. 28 (1995), 214-223.
    MathSciNet     CrossRef

  6. B.- Y. Chen, A report on submanifold of finite type, Soochow J. Math. 22 (1996), 117-337.
    MathSciNet    

  7. S. M. Choi, On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), 351-367.
    MathSciNet    

  8. S. M. Choi, On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), 285-304.
    MathSciNet    

  9. F. Dillen, J. Pas and L. Vertraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J. 13 (1990), 10-21.
    MathSciNet     CrossRef

  10. F. Dillen, J. Pas and L. Vertraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica 18 (1990), 239-246.
    MathSciNet    

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

  12. O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata 34 (1990), 105-112.
    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, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012, 1-28.
    MathSciNet     CrossRef

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

  16. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385.
    MathSciNet     CrossRef

  17. D. W. Yoon, On the Gauss map of translation surfaces in Minkowski 3-space, Taiwanese J. Math. 6 (2002), 389-398.
    MathSciNet    

  18. D. W. Yoon, Some classification of translation surfaces in Galilean 3-space, Int. J. Math. Anal. (Ruse) 6 (2012), 1355-1361.
    MathSciNet    
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