Abstract
In this paper, we study surfaces in E3 whose Gauss map G satisfies the equation □ G = f(G + C) for a smooth function f and a constant vector C, where □ 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 □G = λ(G + C) for a constant λ and a constant vector C.
Original language | English |
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Pages (from-to) | 935-949 |
Number of pages | 15 |
Journal | Bulletin of the Korean Mathematical Society |
Volume | 50 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- □-pointwise 1-type
- Cheng-Yau operator
- Gauss map