伽利略和伪伽利略空间中Mannheim曲线的若干性质

Spacelike and Timelike Admissible Smarandache Curves in Pseudo-Galilean Space

In this paper, space and timelike admissible Smarandache curves in the pseudo- Galilean 3-space are investigated. Also, Smarandache curves of the position vector of space and timelike arbitrary curve and some of its special curves in the pseudo- Galilean 3-space are obtained. To confirm our main results, some examples are given and illustrated.

A study on special curves of AW(k)-type in the pseudo-Galilean space

This paper is devoted to the study of AW(k)-type curves according to the equiform differential geometry of the pseudo-Galilean space. We show that equiform Bertrand curves are circular helices or isotropic circles of the pseudo-Galilean space. Also, there are equiform Bertrand curves of AW(3) and weak AW(3)-types. Moreover, we give the relations between the equiform curvatures of these curves. Finally, examples of some special curves are given and plotted.

Non-zero constant curvature factorable surfaces in pseudo-Galilean space

Factorable surfaces, i.e. graphs associated with the product of two functions of one variable, constitute a wide class of surfaces. Such surfaces in the pseudo-Galilean space with zero Gaussian and mean curvature were obtained in [1]. In this study, we provide new classification results relating to the factorable surfaces with non-zero Gaussian and mean curvature.

Spacelike Curves of Constant-Ratio in Pseudo-Galilean Space

In the theory of differential geometry curves, a curve is said to be of constant-ratio if the ratio of the length of the tangential and normal components of its position vector function is constant. In this paper, we study and characterize a spacelike admissible curve of constant-ratio in terms of its curvature functions in pseudo-Galilean space. Some special curves of constant-ratio such as T and N constant types are investigated. As an application of our main results, some examples are given.

伪伽利略4-空间 $G_{1}^{4}$ 中若干特殊曲线的研究

The investigation of some special curves in the pseudo-Galilean 4-space $G_{1}^{4} $

本文依据曲率函数刻画伪伽利略4-空间 $G_{1}^{4}$ 中的任意容许曲线，并给出位置曲线、从切曲线、斜螺旋线和球面曲线等特殊曲线的分类及充要条件。

四维伪伽利略空间中曲线不可伸缩流与能量的几何视角

A geometric perspective on the inextensible flows and energy of curves in 4-dimensional pseudo-Galilean space

本文从几何视角探讨了四维伪伽利略空间中曲线不可伸缩流的数学表达及其弹性能量函数的构建方法。

Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spaces

In this work, we are interested in the differential geometry of curves in the simply isotropic and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose absolute figure is given by a plane at infinity and a degenerate quadric. Motivated by the success of rotation minimizing (RM) frames in Euclidean and Lorentzian geometries, here we show how to build RM frames in isotropic geometries and apply them in the study of isotropic spherical curves. Indeed, through a convenient manipulation of osculating spheres described in terms of RM frames, we show that it is possible to c…