University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)2676-72603120140701Parallel Transport Frame in 4 -dimensional Euclidean Spaceترابری موازی قابی در فضای اقلیدسی چهار بعدی91103498ENF.GÖKÇELIKDepartment of Mathematics, Faculty of Science, University of Ankara Tandogan,
Ankara, TURKEYZ.BOZKURTDepartment of Mathematics, Faculty of Science, University of Ankara Tandogan,
Ankara, TURKEYI.GÖKDepartment of Mathematics, Faculty of Science, University of Ankara Tandogan,
Ankara, TURKEYN.EKMEKCIDepartment of Mathematics, Faculty of Science, University of Ankara Tandogan,
Ankara, TURKEYY.YAYLIDepartment of Mathematics, Faculty of Science, University of Ankara Tandogan,
Ankara, TURKEYJournal Article20130510In this work, we give parallel transport frame of a curve and we <br />introduce the relations between the frame and Frenet frame of the curve in <br />4-dimensional Euclidean space. The relation which is well known in Euclidean <br />3-space is generalized for the rst time in 4-dimensional Euclidean space. <br />Then we obtain the condition for spherical curves using the parallel transport <br />frame of them. The condition in terms of { and is so complicated but in <br />terms of k1 and k2 is simple. So, parallel transport frame is important to make <br />easy some complicated characterizations. <br />Moreover, we characterize curves whose position vectors lie in their nor- <br />mal, rectifying and osculating planes in 4-dimensional Euclidean space E4:
http://cjms.journals.umz.ac.ir/article_498_73f8d022f61f4fd6d31bc0c4b0d8bfb2.pdf