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CLASSIFICATIONS OF ROTATION SURFACES IN PSEUDO-EUCLIDEAN SPACE

  • Kim, Young-Ho (Department of Mathematics College of Natural Sciences Kyungpook National University) ;
  • Yoon, Dae-Won (Department of Mathematics Education and RINS Gyeongsang National University)
  • Published : 2004.03.01

Abstract

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

Keywords

References

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  2. Spacelike Rotational Surfaces of Elliptic, Hyperbolic and Parabolic Types in Minkowski Space E 1 4 ${E^{4}_{1}}$ with Pointwise 1-Type Gauss Map vol.17, pp.1-2, 2014, https://doi.org/10.1007/s11040-014-9153-6
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