Parallel Transport Frame in 4-dimensional Euclidean Space
Abstract
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 first 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 \kappa and {\tau} is so complicated but in terms of k_{1} and k_{2} is simple. So, parallel transport frame is important to make easy some complicated characterizations. Moreover, we characterize curves whose position vectors lie in their normal, rectifying and osculating planes in 4-dimensional Euclidean space E^{4}.
Cite
@article{arxiv.1207.2999,
title = {Parallel Transport Frame in 4-dimensional Euclidean Space},
author = {Fatma Gökçelik and Zehra Bozkurt and İsmail Gök and F. Nejat Ekmekci and Yusuf Yayli},
journal= {arXiv preprint arXiv:1207.2999},
year = {2012}
}
Comments
13 pages, 3 figures