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ON ROTATION SURFACES IN THE MINKOWSKI 3-DIMENSIONAL SPACE WITH POINTWISE 1-TYPE GAUSS MAP

  • Published : 2004.11.01

Abstract

In this paper, we study rotation surfaces in the Minkowski 3-dimensional space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem concerning rotation surfaces and constancy of the mean curvature of certain open subsets on these surfaces.

Keywords

References

  1. L. J. Alias, A. Ferrandez, P. Lucas and M. A. Meronno, On the Gauss map of B-scrolls, Tsukuba J. Math. 22 (1998), 317–377.
  2. B.-Y. Chen, submanifolds of finite type, Soochow J. Math. 9 (1987), 65–81.
  3. B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore, 1984.
  4. B.-Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc. 35 (1987), 161–186. https://doi.org/10.1017/S0004972700013162
  5. S. M. Choi, On the Gauss map of ruled surfaces in a three-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), 285–304. https://doi.org/10.21099/tkbjm/1496162870
  6. M. Choi and Y. H. Kim, Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map, Bull. Korean Math. Soc. 38 (2001), no. 4, 753–761.
  7. Jun-ichi Hano and K. Nomizu, On Isometric immersions of the hyperbolic plane into the Lorentz-Minkowski space and the Monge-Ampre equation of a certain type, Math. Ann. 262 (1983), 245–253. https://doi.org/10.1007/BF01455315
  8. Y. H. Kim and D. W. Yoon, Ruled surfaces with pointwise 1-type Gauss map, J. Geom. Phys. 34 (2000), 191–205. https://doi.org/10.1016/S0393-0440(99)00063-7
  9. A. Niang, Rotation surfaces with pointwise 1-type Gauss map (submitted for publication in 2003).

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  4. Helicoidal surfaces satisfying $${\Delta ^{II}\mathbf{G}=f(\mathbf{G}+C)}$$ Δ II G = f ( G + C ) vol.107, pp.3, 2016, https://doi.org/10.1007/s00022-015-0284-0