Abstract
In this work, we study the canal surfaces foliated by pseudo spheres S12 along a Frenet curve in terms of their Gauss maps in Minkowski 3-space. Such kind of surfaces with pointwise 1-type Gauss maps are classified completely. For example, the canal surface with proper pointwise 1-type Gauss map of the first kind if and only if it is a part of a minimal surface of revolution.
Highlights
In the theory of surface, a kind of surface called canal surfaces will shaped by sweeping a family of spheres whose centers lie on a space curve in Euclidean 3-space
1-type Gauss map of the first kind if and only if it is a part of a minimal surface of revolution
In Minkowski 3-space, a canal surface can be formed as the envelope of a family of pseudo-Riemannian space forms, i.e., pseudo spheres S21, pseudo hyperbolic spheres H20 and lightlike cones Q2 [4,5,6]
Summary
In the theory of surface, a kind of surface called canal surfaces will shaped by sweeping a family of spheres whose centers lie on a space curve in Euclidean 3-space. Euclidean space) whose Gauss map G satisfies ∆G = f (G + C ) is said to have pointwise 1-type Gauss map for a non-zero smooth function f and a constant vector C, where ∆ is the Laplacian defined on M stated by. Based on the conclusions obtained in [1], the canal surface with pointwise 1-type Gauss map is discussed in [2]. In order to do further and complete geometric investigation for canal surfaces in Minkowski 3-space, the canal surfaces foliated by pseudo spheres S21 along Frenet curves to be studied in the present work. The surfaces are smooth, regular, topologically connected unless otherwise stated in this paper
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