A NOTE ON SPECIAL CURVES IN E^4

Abstract

This article has consisted of a part of doctorate thesis by Süha Yılmaz [7]. Firstly, Frenet formulas are given in E^4. Later, characterizations of regular and inclined curves are studied E^4. It has been given that a space-like curve is an inclined curve if and only if theexpression..........obtained using harmonic curvature functions in E^4. In addition, it has been observed that a fifth order vectorial differential equation of position vector of a space-like curve in E^4 been satisfied by means of Frenet formulas. Similarly, it has been denoted that a fourth order vectorial differential equation of tangent vector of a space-like curve in E^4 has been also verified using Frenet formulas. Moreover, we characterized tangent and trinormal indicatrices with one theorem. Finally, it has been denoted that if and only if spherical indicatrices of space-like curve with time-like trinormal vector are regular curves.