Parallel Transport Frame of Smarandache Curves in Euclidean Space

In the present work, we introduce Parallel transport frames of Smarandache curves in Euclidean space. In the first section, we give the basic tools of a parallel transport frame of a curve in 4-dimensional Euclidean space. In the second section, we study Smarandache curve of Euclidean space in parallel transport frame, we solve a few theorems, corollaries and examples. Again third section, we define parallel transport frame to the Smarandache curve and obtain some definitions and their apparatus. Further fourth section, we have also explained to Frenet frame of principal normal, binomial and their derivatives in the curvatures of the curve. In the end section, we discussed about the Smarandache curve in the Euclidean space of all apparatus Frenet-Serret in the differential geometry.