Search

Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term "equiform parameter (EQP)", "equiform frame", and "equiform formulas (EQF)" in regard to the Minkowski three-space. Second, we define spacelike normal curves (SPN) in Minkowski three-space and present a variety of descriptions of these curves with equiform spacelike (EQS) or equiform timelike (EQN) principal normals in Minkowski three-space. Third, we discuss the implications of these findings. Finally, an example is given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This work aims at investigating the geometry of surfaces corresponding to the geometry of solutions of the vortex filament equation in Euclidean 3-space E 3 using the quasi-frame. In particular, we discuss some geometric properties and some characterizations of parameter curves of these surfaces in E 3 . [ABSTRACT FROM AUTHOR]

This work aims at studying resolutions of the jerk and snap vectors of a point particle moving along a quasi curve in Euclidean 3-space E 3 . In particular, we obtain the resolution of the jerk and snap vectors along the quasi vectors and offer an alternative resolution of the jerk and snap vectors along the tangential direction and two special radial directions that lie in the osculating and rectifying planes. This alternative resolution for a quasi plane curve in Euclidean 3-space E 3 is given as corollary. Moreover, our results are illustrated via some examples. [ABSTRACT FROM AUTHOR]