Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All superconformal surfaces in \R^4 in terms of minimal surfaces   We give an explicit construction of any simply-connected superconformal
surface $\phi\colon M^2\to \R^4$ in Euclidean space in terms of a pair of
conjugate minimal surfaces $g,h\colon M^2\to\R^4$. That $\phi$ is
superconformal means that its ellipse of curvature is a circle at any point. We
characterize the pairs $(g,h)$ of conjugate minimal surfaces that give rise to
images of holomorphic curves by an inversion in $\R^4$ and to images of
superminimal surfaces in either a sphere $\Sf^4$ or a hyperbolic space $\Hy^4$
by an stereographic projection. We also determine the relation between the
pairs $(g,h)$ of conjugate minimal surfaces associated to a superconformal
surface and its image by an inversion. In particular, this yields a new
transformation for minimal surfaces in $\R^4$.

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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-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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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: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg