Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative minimal embeddings and morphisms of pseudo-Riemannian
  calculi   In analogy with classical submanifold theory, we introduce morphisms of real
metric calculi together with noncommutative embeddings. We show that basic
concepts, such as the second fundamental form and the Weingarten map, translate
into the noncommutative setting and, in particular, we prove a noncommutative
analogue of Gauss equations for the curvature of a submanifold. Moreover, the
mean curvature of an embedding is readily introduced, giving a natural
definition of a noncommutative minimal embedding, and we illustrate the novel
concepts by considering the noncommutative torus as a minimal surface in the
noncommutative 3-sphere.

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The categories of this paper are: q-bio
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat