Generalized Bertrand Curve Pairs in Euclidean Four-Dimensional Space
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. Furthe...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/4/253 |
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| Summary: | 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. |
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| ISSN: | 2075-1680 |