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.
In this work, a family of ruled surfaces named generalized null scrolls in Minkowski 3-space are investigated via the defined structure functions. The relations between the base curve and the ruling flow of the generalized null scroll are revealed. The Gaussian curvature, mean curvature, second Gaussian curvature and the second mean curvature are given and related to each other. Last but not least, the generalized null scrolls whose base curves are k-type null helices are discussed and several examples are presented.
In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail.
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