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

Title & Authors
SURFACES IN $\small{\mathbb{E}^3}$ WITH L1-POINTWISE 1-TYPE GAUSS MAP
Kim, Young Ho; Turgay, Nurettin Cenk;

Abstract
In this paper, we study surfaces in $\small{\mathb{E}^3}$ whose Gauss map G satisfies the equation $\small{{\Box}G=f(G+C)}$ for a smooth function $\small{f}$ and a constant vector C, where $\small{{\Box}}$ 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 $\small{{\Box}G={\lambda}(G+C)}$ for a constant $\small{{\lambda}}$ and a constant vector C.
Keywords
Gauss map;$\small{{\Box}}$-pointwise 1-type;Cheng-Yau operator;
Language
English
Cited by
1.
CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP,;;

대한수학회보, 2013. vol.50. 4, pp.1345-1356
2.
RULED SURFACES AND GAUSS MAP,;

대한수학회보, 2015. vol.52. 5, pp.1661-1668
1.
Cheng–Yau Operator and Gauss Map of Surfaces of Revolution, Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39, 4, 1319
2.
Classifications of Canal Surfaces with L1-Pointwise 1-Type Gauss Map, Milan Journal of Mathematics, 2015, 83, 1, 145
3.
RULED SURFACES AND GAUSS MAP, Bulletin of the Korean Mathematical Society, 2015, 52, 5, 1661
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