Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

SURFACES OF REVOLUTION WITH LIGHT-LIKE AXIS

  • Yoon, Dae Won (Department of Mathematics Education and RINS Gyeongsang National University) ;
  • Lee, Chul Woo (Department of Mathematics Education Gyeongsang National University)
  • Published : 2012.11.15
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the surfaces of revolution with light-like axis satisfying some equation in terms of a position vector field and the Laplacian with respect to the non-degenerate third fundamental form in Minkowski 3-space. As a result, we give some special example of the surfaces of revolution with light-like axis.

Keywords

References

  1. C. Baikoussis and D. E. Blair, On the Gauss map of ruled surfaces, Glasgow Math. J. 34 (1992), 355-359. https://doi.org/10.1017/S0017089500008946
  2. C. Baikoussis and L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Sem. Math. Messina Ser. II 16 (1993), 31-42.
  3. C. Baikoussis and L. Verstraelen, The Chen-type of the spiral surfaces, Result Math. 28 (1995), 214-223. https://doi.org/10.1007/BF03322254
  4. B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), 117-337.
  5. S. M. Choi, On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), 285-304. https://doi.org/10.21099/tkbjm/1496162870
  6. S. M. Choi, On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), 351-367. https://doi.org/10.21099/tkbjm/1496162874
  7. F. Dillen, J. Pas and L. Verstraelen, On the Gauss map of surfaces of revolution, Bull. Insto. Math. Acad. Sinica 18 (1990), 239-249.
  8. O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata 34 (1990), 105-112.
  9. G. Kaimakamis and B, Papantoniou, Surfaces of revolution in the 3- dimensional Lorentz-Minkowski space satisfying ${\Delta}^{II}{^{\rightarrow}_r}\;=\;A{^{\rightarrow}_r}$, J. Geom. 81 (2004), 81-92. https://doi.org/10.1007/s00022-004-1675-9
  10. G. Kaimakamis, B. Papantoniou and K. Petoumenos, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space $\mathbb{E}^3_1$ satisfying ${\Delta}^{III}{^{\rightarrow}_r}\;=\;A{^{\rightarrow}_r}$, Bull. Greek Math. Soc. 50 (2005), 75-90.
  11. Y. H. Kim, C. W. Lee and D. W. Yoon, On the Gauss map of surfaces of revolution without parabolic points, Bull. Korean Math. Soc. 46 (2009), 1141-1149. https://doi.org/10.4134/BKMS.2009.46.6.1141
  12. C. W. Lee, Y. H. Kim and D. W. Yoon, Ruled surfaces of non-degenerate third fundamental forms in Minkowski 3-spaces, Appl. Math. Computation 216 (2010), 3200-3208. https://doi.org/10.1016/j.amc.2010.04.043
  13. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. https://doi.org/10.2969/jmsj/01840380