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arXiv · 1207.2999

Parallel Transport Frame in 4-dimensional Euclidean Space

Fatma Gökçelik·Zehra Bozkurt·İsmail Gök·F. Nejat Ekmekci·Yusuf Yayli
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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 κand τ 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}.

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Fatma Gökçelik, Zehra Bozkurt, İsmail Gök, F. Nejat Ekmekci, Yusuf Yayli. 2012-07-12. Parallel Transport Frame in 4-dimensional Euclidean Space. https://arxiv.org/abs/1207.2999

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