CHAPTER I INTRODUCTION
A well-known theorem on space curves is the Fundamental Theorem.
This theorem states th at i f two real-valued functions
= *1 (ธ) '■=* 0 , kg ะ= k2(ร) > 0
defined on an in terv al jo.LJ are given, where the function k^ is of class C^ and the function k2 is of class C^, then there ex ists a space curve for which k^ is the curvature and kg is the to rsio n , and ร is the arc length measured from some su itable base p o in t. Such a curve, is uniquely determined up to a Euclidean motion.
In th is study we sh all extend th is theorem to curves in Euclidean ท-space.
Chapter II deals with the relevant d efin itio n s and some important theorems of vector calculus needed in our study. Chapter III deals with Euclidean n-space, lin ear v a rie tie s, and Euclidean motions of Rn . We characterize the Frenet-frame and the curvatures of curves in
Euclidean n-space in Chapter IV. Chapter V states and proves Fundamental Existence Theorem for curve in Euclidean n-space.
