An Examination on $\ NP^{\ast }$ Curves in $E^3$

Abstract

The evolute and involute curves, Mannheim curves or Bertrand curves are the famous examples of the associated curve pairs. In the view of such information we have defined $ NP^{\ast }$ curve pairs where the principal normal vector of the first curve and the vector $P^{\ast }$  lying on the normal plane of the second curve are linearly dependent. We have called these curve pairs $NP^{\ast }-$ curves. Second curve is named $NP^{\ast }-$ partner curve. Also, while the examination of $NP^{\ast }-$ curves we obtain some relations for the curvatures and Frenet apparatus of the second curve based on the Frenet apparatus of the first curve.

Keywords

• Darboux vector
• Offset curves
• Mannheim curves
• Bertrand pairs

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