Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Equivalence Problem of Curves in a Riemannian Manifold   The equivalence problem of curves with values in a Riemannian manifold, is
solved. The domain of validity of Frenet's theorem is shown to be the spaces of
constant curvature. For a general Riemannian manifold new invariants must thus
be added. There are two important generic classes of curves; namely, Frenet
curves and a new class, called curves "in normal position". They coincide in
dimensions $\leq 4$ only. A sharp bound for asymptotic stability of
differential invariants is obtained, the complete systems of invariants are
characterized, and a procedure of generation is presented. Different classes of
examples (specially in low dimensions) are analyzed in detail.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
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The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg