Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Transport Frame in 4-dimensional Euclidean Space   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}.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg