Principal normal indicatrix (N) of curves according to their alternative frames in Euclidean 3-space

Abstract

In this paper, we define a new family of curves called principal normal indicatrix (briefly, PNI) of space curves with unit speed in 3-dimensional Euclidean space. During the definition, we use alternative frames and we give some conditions for space curves to be general helix, slant helix, plane curve or involute curve.