Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tractors and Tractrices in Riemannian Manifolds   We generalize the notion of planar bicycle tracks -- a.k.a. one-trailer
systems -- to so-called tractor/tractrix systems in general Riemannian
manifolds and prove explicit expressions for the length of the ensuing
tractrices and for the area of the domains that are swept out by any given
tractor/tractrix system. These expressions are sensitive to the curvatures of
the ambient Riemannian manifold, and we prove explicit estimates for them based
on Rauch's and Toponogov's comparison theorems. Moreover, the general length
shortening property of tractor/tractrix systems is used to generate geodesics
in homotopy classes of curves in the ambient manifold.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas