Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural parameterizations of closed projective plane curves   A natural parametrization of smooth projective plane curves which tolerates
the presence of sextactic points is the Forsyth-Laguerre parametrization. On a
closed projective plane curve, which necessarily contains sextactic points,
this parametrization is, however, in general not periodic. We show that by the
introduction of an additional scalar parameter $\alpha \leq \frac12$ one can
define a projectively invariant $2\pi$-periodic global parametrization on every
simple closed convex sufficiently smooth projective plane curve without
inflection points. For non-quadratic curves this parametrization, which we call
balanced, is unique up to a shift of the parameter. The curve is an ellipse if
and only if $\alpha = \frac12$, and the value of $\alpha$ is a global
projective invariant of the curve. The parametrization is equivariant with
respect to duality.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph