  In this paper, we introduce an inclined curves according to parallel
transport frame. Also, we define a vector field called Darboux vector field of
an inclined curve in and we give a new characterization such as: "\alpha: I
\subset R \rightarrow E^4 is an inclined curve \Leftrightarrow k_1 \int k_1ds +
k_2 \int \k_2 +k_3ds = 0" where k_1, k_2, K_3 are the principal curvature
functions according to parallel transport frame of the curve and we give the
similar characterizations such as "\alpha : I \subset R \rightarrow E^3 is a
generalized helix \Leftrightarrow k_1 \int k_1ds + k_2 \int k_2ds = 0" where
k_1, k_2 are the principal curvature functions according to Bishop frame of the
curve \alpha. Moreover, we illustrate some examples and draw their figures with
Mathematica Programme.
