Parallel Transport Frame in 4 -dimensional Euclidean Space

Document Type: Research articles


Department of Mathematics, Faculty of Science, University of Ankara Tandogan, Ankara, TURKEY


In this work, we give parallel transport frame of a curve and we
introduce the relations between the frame and Frenet frame of the curve in
4-dimensional Euclidean space. The relation which is well known in Euclidean
3-space is generalized for the …rst time in 4-dimensional Euclidean space.
Then we obtain the condition for spherical curves using the parallel transport
frame of them. The condition in terms of { and  is so complicated but in
terms of k1 and k2 is simple. So, parallel transport frame is important to make
easy some complicated characterizations.
Moreover, we characterize curves whose position vectors lie in their nor-
mal, rectifying and osculating planes in 4-dimensional Euclidean space E4: