In this article, we investigate the relationships between the instantaneous invariants of a one-
parameter spatial movement and the local invariants of the axodes. Specifically, we provide …

E. Study map is one of the most basic and powerful mathematical tools to study lines in line
geometry, it has symmetry property. In this paper, based on the E. Study map, clear …

Symmetry is a frequently recurring theme in mathematics, nature, science, etc. In
mathematics, its most familiar manifestation appears in geometry, most notably line …

This paper derives the declarations for timelike ruled surfaces with stationary timelike Disteli-
axis by the E. Study map. This prepares the ability to determine a set of Lorentzian invariants …

A timelike (TL) constant axis ruled surface in E 1 3 (Minkowski 3-space), as determined by its
ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this …

In this paper, based on the E. Study map, direct appearances were sophisticated for one-
parameter hyperbolic dual spherical locomotions and invariants of the axodes. With the …

In this paper, we investigate null Cartan geodesic isophote curves in the Minkowski 3-space,
and give examples where such curves actually exist. By categorizing the types of light …

In this paper, based on the E. Study map, clear terms are offered for the differential
equations of one-parameter Lorentzian spatial kinematics that are coordinate system …

The association between the instantaneous invariants of a one-parameter Lorentzian spatial
movement and the spacelike lines with certain trajectories is considered in this study. To be …

We considered differential geometries of helical curves for ruled and developable surfaces
in Euclidean 3-space E 3. We clarify the conditions for ruled surface to become stationary …