Partner Curves in Three Dimensional Degenerated Space Form

Year 2024, , 213 - 220, 23.04.2024

Huili Liu , Yixuan Liu

https://doi.org/10.36890/iejg.1466320

Abstract

Using elementary and effective methods we study cone curves and their associated curves or partner curves
in the three dimensional lightlike cone $\Q^3$, which is called three dimensional degenerated space form of the four dimensional Minkowski space $\E^4_1$.
We define the associated curve of the cone curve and also partner curves of
some special curves, such as a Bertrand curve and a Mannheim curve.
We consider the properties and
relations of a curve and its associated curve or partner curve.
Some geometric characterizations of these curves are also given.

Keywords

Degenerated space form, cone curve, curvature and torsion, associated curve, partner curve

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