Surfaces in E3 with L1-pointwise 1-type Gauss map
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초록
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 and a constant vector C.
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 and a constant vector C.
참고문헌 (20)
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