Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete version of the Darboux transform for isothermic surfaces   We study Christoffel and Darboux transforms of discrete isothermic nets in
4-dimensional Euclidean space: definitions and basic properties are derived.
Analogies with the smooth case are discussed and a definition for discrete
Ribaucour congruences is given. Surfaces of constant mean curvature are special
among all isothermic surfaces: they can be characterized by the fact that their
parallel constant mean curvature surfaces are Christoffel and Darboux
transforms at the same time. This characterization is used to define discrete
nets of constant mean curvature. Basic properties of discrete nets of constant
mean curvature are derived.

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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: physics