Characterizations of the Quaternionic Mannheim Curves in E^4
O. Zeki Okuyucu
TL;DR
This paper introduces quaternionic Mannheim curves and provides characterizations of these curves in both 3D and 4D Euclidean spaces, expanding the understanding of their geometric properties.
Contribution
It defines quaternionic Mannheim curves and offers new characterizations in Euclidean 3-space and 4-space, extending previous work on Mannheim curves.
Findings
Characterizations of quaternionic Mannheim curves in E^3 and E^4
Extension of Mannheim curve theory to quaternionic setting
New geometric properties identified for these curves
Abstract
In [5], Matsuda and Yorozo obtained that Mannheim curves in 4-dimensional Euclidean space. In this study, we define quaternionic Mannheim curves and we give some characterizations of them in Euclidean 3-space and 4-space.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Advanced Differential Geometry Research · Noncommutative and Quantum Gravity Theories