A new characterization of curves in Euclidean $4$-space $\mathbb E^4$

In the present study, we characterize a regular curve whose position vector can be written as a linear combination of its Serret–Frenet vectors in Euclidean $4$-space $\mathbb E^4$. We investigate such curves in terms of their curvature functions. Further, we obtain some results of $T$-constant, $N$-constant and constant ratio curves in $\mathbb E^4$.