Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE II

  • Choi, Mie-Kyung (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY) ;
  • Kim, Young-Ho (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY) ;
  • Park, Gi-Chan (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
  • Published : 2009.05.31
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Abstract

We classify and characterize the rational helicoidal surfaces in a three-dimensional Minkowski space satisfying pointwise 1-type like problem on the Gauss map.

Keywords

References

  1. C. Baikoussis and L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Sem. Mat. Messina Ser. II 2(16) (1993), 31–42
  2. C. C. Beneki, G. Kaimakamis, and B. J. Papantoniou, Helicoidal surfaces in threedimensional Minkowski space, J. Math. Anal. Appl. 275 (2002), no. 2, 586–614 https://doi.org/10.1016/S0022-247X(02)00269-X
  3. B.-Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics, 1. World Scientific Publishing Co., Singapore, 1984
  4. M. Choi, D. S. Kim, and Y. H. Kim, Helicoidal surfaces with pointwise 1-type Gauss map, to appear in J. Korean Math. Soc https://doi.org/10.4134/JKMS.2009.46.1.215
  5. M. Choi, Y. H. Kim, H. Liu, and D. W. Yoon, Helicoidal surfaces and their Gauss map in Minkowski 3-space, submitted for publication
  6. F. Ji and Z. H. Hou, Helicoidal surfaces under the cubic screw motion in Minkowski 3-space, J. Math. Anal. Appl. 318 (2006), no. 2, 634–647 https://doi.org/10.1016/j.jmaa.2005.06.032
  7. Y. H. Kim and D. W. Yoon, Classification of ruled surfaces in Minkowski 3-spaces, J. Geom. Phys. 49 (2004), no. 1, 89–100 https://doi.org/10.1016/S0393-0440(03)00084-6
  8. Y. H. Kim and D. W. Yoon, On the Gauss map of ruled surfaces in Minkowski space, Rocky Mountain J. Math. 35 (2005), no. 5, 1555–1581

Cited by

  1. Mean curvatures and Gauss maps of a pair of isometric helicoidal and rotation surfaces in Minkowski 3-space vol.368, pp.2, 2010, https://doi.org/10.1016/j.jmaa.2010.03.054
  2. HELICOIDAL SURFACES OF THE THIRD FUNDAMENTAL FORM IN MINKOWSKI 3-SPACE vol.52, pp.5, 2015, https://doi.org/10.4134/BKMS.2015.52.5.1569
  3. CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1345