Surfaces in $\mathbb E^3$ with $L_1$-pointwise 1-type Gauss map
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 935-949
https://doi.org/10.4134/BKMS.2013.50.3.935
Printed May 31, 2013
Young Ho Kim and Nurett$\dot{\text i}$n Cenk Turgay
Kyungpook National University, Istanbul Technical University
Abstract : In this paper, we study surfaces in $\mathbb E^3$ whose Gauss map $G$ satisfies the equation $\square G=f(G+C)$ for a smooth function $f$ and a constant vector $C$, where $\square$ 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 $\square G=\lambda(G+C)$ for a constant $\lambda$ and a constant vector $C$.
Keywords : Gauss map, $\square$-pointwise 1-type, Cheng-Yau operator
MSC numbers : 53B25, 53C40
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