Partner Curves in Three Dimensional Degenerated Space Form

Authors : Huili Liu, Yixuan Liu

Pages : 213-220

Doi:10.36890/iejg.1466320

View : 38 | Download : 49

Publication Date : 2024-04-23

Article Type : Research Paper

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