The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

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International Electronic Journal of Geometry
Volume:16 Issue:1
The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

Authors : Tülay ERİŞİR, Zeynep İSABEYOĞLU

Pages : 111-121

Doi:10.36890/iejg.1210442

View : 58 | Download : 8

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :In this paper, the spinor formulations of Mannheim curve pair are investigated. First of all, two spinors matching to Mannheim curve pair are given and by considering the relationships between the Frenet frames of Mannheim curve pair, the relationship between two spinors matching to this curve pair are gotten. Therefore, a geometric interpretations of spinors are obtained using the Mannheim curve pair and considering Mannheim curve as helix the spinor formulations of Mannheim curve pair are given. Moreover, the spinor formulations are also obtained for the curvatures of the Mannheim curve pair. Consequently, an example of these spinors is obtained. Therefore, it is thought that this study will make an important contribution to the mathematical analysis and geometric interpretation of spinors, which have many uses in physics.
Keywords : Spinors, Clifford Algebra, Euclidean space, Mannheim curve pair

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