J. Korean Math. Soc. 2004; 41(2): 379-396
Printed March 1, 2004
Copyright © The Korean Mathematical Society.
Young Ho Kim and Dae Won Yoon
Kyungpook National University, Gyeongsang National University
In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space $\Bbb E^4_2$. 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: rotation surfaces, Gauss map, finite type, Pseudo-Eucli-dean space
MSC numbers: 53B25, 53C50
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