Generalized Bertrand Curve Pairs in Euclidean Four-Dimensional Space
Year: 2025
Type: article
Abstract: In this study, the existence of Bertrand curves (in the classical sense, i.e., curves with a common principal normal vector field) in four-dimensional Euclidean space is demonstrated using a novel approach. The necessary conditions for a regular curve to be a Bertrand curve pair are obtained. Furthermore, the relationship between Bertrand curves and Combescure-related curves (pairs of curves with parallel Frenet vectors) is established, and several geometric properties are derived. Additionally, examples are constructed for both Bertrand curve pairs and Combescure-related curve pairs, and their orthogonal projections onto three-dimensional subspaces of four-dimensional space are visualized.
Source: Axioms
Authors: Yanlin Li, Osman Keçilioğlu, Kazım İlarslan
Institutions: Hangzhou Normal University, Kırıkkale University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4408925415