Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian submanifolds of the nearly K\"ahler $\mathbb{S}^3 \times
  \mathbb{S}^3$ from minimal surfaces in $\mathbb{S}^3$   We study non-totally geodesic Lagrangian submanifolds of the nearly K\"ahler
$\mathbb{S}^3 \times \mathbb{S}^3$ for which the projection on the first
component is nowhere of maximal rank. We show that this property can be
expressed in terms of the so called angle functions and that such Lagrangian
submanifolds are closely related to minimal surfaces in $\mathbb{S}^3$. Indeed,
starting from an arbitrary minimal surface, we can construct locally a large
family of such Lagrangian immersions, including one exceptional example.

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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph