On Mannheim Partner Curves of $AW(k)-$type

Abstract

In this study, firstly, Mannheim curves with ${\kappa }_1(s)\ne 0$, ${\kappa }_2(s)\ne 0$ 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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