Some Characterizations of Special Curves in the Euclidean Space $\mathrm{E}^4$
Melih Turgut, Ahmad T Ali
TL;DR
This paper explores the properties and characterizations of special curves such as helices, ccr curves, and involutes in four-dimensional Euclidean space, providing new relations among their invariants.
Contribution
It offers novel characterizations of helices, ccr curves, and involutes in E^4, along with relations among Frenet-Serret invariants of Bertrand curves.
Findings
Characterizations of helices and ccr curves in E^4
Relations among Frenet-Serret invariants of Bertrand curves
New characterizations of involutes of helices
Abstract
In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.
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Taxonomy
TopicsMathematics and Applications · Advanced Mathematical Theories and Applications · Algebraic and Geometric Analysis