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http://dx.doi.org/10.4134/BKMS.2013.50.3.935

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

Kim, Young Ho (Department of Mathematics Kyungpook National University)
Turgay, Nurettin Cenk (Department of Mathematics Istanbul Technical University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 935-949 More about this Journal
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.
Keywords
Gauss map; ${\Box}$-pointwise 1-type; Cheng-Yau operator;
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Times Cited By KSCI : 2  (Citation Analysis)
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