Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Willmore Legendrian surfaces in pseudoconformal 5-sphere   Let $ X: M \hook S^5$ be a compact Legendrian surface in pseudoconformal(CR)
5-sphere. We introduce a pseudoconformally invariant Willmore type second order
functional $ \W(X)$, and study its critical points called Willmore Legendrian
surfaces. The fifth order structure equations show that Willmore dual can be
defined for a class of Willmore Legendrian surfaces. Moreover when this dual is
constant, Willmore Legendrian surface admits a Weierstra\ss type representation
in terms of immersed meromorphic curve in $ \C^2$ satisfying an appropriate
real period condition via pseudoconformal stereographic projection. We show
that every compact Riemann surface admits a generally one to one, conformal,
Willmore Legendrian immersion in $ S^5$ with constant Willmore dual. As a
corollary, every compact Riemann surface can be conformally immersed in $ \C^2$
as an exact, algebraic Lagrangian surface.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat