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

preprint2011arXivOpen access

In this study, firstly, Mannheim curves with $κ_1 (s) \ne 0$ , $κ_2 (s) \ne 0$ 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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On Mannheim Partner Curves of $AW(k)-$ type

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