Abstract
Canal surfaces are defined and divided into nine types in Minkowski 3-space E 1 3 , which are obtained as the envelope of a family of pseudospheres S 1 2 , pseudohyperbolic spheres H 0 2 , or lightlike cones Q 2 , whose centers lie on a space curve (resp. spacelike curve, timelike curve, or null curve). This paper focuses on canal surfaces foliated by pseudohyperbolic spheres H 0 2 along three kinds of space curves in E 1 3 . The geometric properties of such surfaces are presented by classifying the linear Weingarten canal surfaces, especially the relationship between the Gaussian curvature and the mean curvature of canal surfaces. Last but not least, two examples are shown to illustrate the construction of such surfaces.
Highlights
The concept of canal surface is the envelope of a moving sphere whose centers lie on a space curve, and their radius varies depending on this curve in Euclidean 3-space E3
Similar to the generating process of canal surfaces in E3, a canal surface in Minkowski 3-space E31 can be obtained as the envelope of a family of pseudospheres S21, pseudohyperbolic spheres H20, or lightlike cones Q2 whose centers lie on a space curve
As a follow-up work of [7], in this paper we focus on the geometric properties of canal surfaces foliated by pseudohyperbolic spheres H20 along three kinds of space curves in E31
Summary
The concept of canal surface is the envelope of a moving sphere whose centers lie on a space curve, and their radius varies depending on this curve in Euclidean 3-space E3. The authors discussed canal surfaces foliated by pseudospheres along three kinds of space curves in E31 [7]. As a follow-up work of [7], in this paper we focus on the geometric properties of canal surfaces foliated by pseudohyperbolic spheres H20 along three kinds of space curves in E31. Different kinds of linear Weingarten canal surfaces are explored, the developable, minimal and umbilical canal surfaces are discussed at the same time. The applications of these surfaces in shape control are important hopefully motivated. Some common results for canal surfaces are shown (Theorems 13 and 14)
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