On Mannheim Partner Curves of $AW(k)-$type
Soley Ersoy, Melek Masal, Murat Tosun
TL;DR
This paper investigates Mannheim curves with non-zero curvature functions, establishing conditions under which they are slant helices and belong to specific AW(k)-types, while also proving the non-existence of AW(1)-type Mannheim curves.
Contribution
It provides new characterizations of Mannheim curves related to AW(k)-types and identifies conditions for their geometric properties.
Findings
Mannheim curves with non-zero curvatures can be slant helices under certain conditions.
Necessary and sufficient conditions for Mannheim curves to be AW(2), AW(3), and weak AW(2)-types are established.
No Mannheim curve of AW(1)-type exists.
Abstract
In this study, firstly, Mannheim curves with , are considered and the conditions are obtained for Mannheim curve to be slant helix. Moreover, the necessary and sufficient conditions are investigated for Mannheim curve to be AW(2), AW(3) and weak AW(2)-types, respectively. Lastly, it is shown that there is no such a Mannheim curve of AW(1)-type.
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Taxonomy
TopicsFinite Group Theory Research