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 theassociated curve pairs. In the view of such information we have defined $NP^ast$curve pairs where the principal normalvector 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 theexamination of $NP^ast$− curves we obtain some relations for the curvatures and Frenet apparatus of the second curvebased on the Frenet apparatus of the first curve