SOME CHARACTERIZATIONS OF OSCULATING CURVES IN THE EUCLIDEAN SPACES

摘要

In this paper, we give some characterization for a osculating curve in 3-dimensional Euclidean space and we define a osculating curve in the Euclidean 4-space as acurve whose position vector always lies in orthogonal complement B_1~⊥of its first binormalvector field B1. In particular, we study the osculating curves in E~4and characterize suchcurves in terms of their curvature functions.