Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star Mean Curvature Flow on 3 manifolds and its B\"acklund
  Transformations   The Hodge star mean curvature flow on a 3-dimensional Riemannian or
pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in
geometric analysis. A curve flow is integrable if the local differential
invariants of a solution to the curve flow evolve according to a soliton
equation. In this paper, we show that this flow on $\mathbb{S}^3$ and
$\mathbb{H}^3$ are integrable, and describe algebraically explicit solutions to
such curve flows. The Cauchy problem of the curve flows on $\mathbb{S}^3$ and
$\mathbb{H}^3$ and its B\"acklund transformations follow from this
construction.

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The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn