Bulletin of the Korean Mathematical Society (대한수학회보)

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SURFACES IN $\mathbb{E}^3$ WITH L1-POINTWISE 1-TYPE GAUSS MAP

  • Received : 2012.04.18
  • Published : 2013.05.31
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Abstract

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

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References

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