Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauss maps of the Ricci-mean curvature flow   In this paper, we investigate the Gauss maps of a Ricci-mean curvature flow.
A Ricci-mean curvature flow is a coupled equation of a mean curvature flow and
a Ricci flow on the ambient manifold. Ruh and Vilms proved that the Gauss map
of a minimal submanifold in a Euclidean space is a harmonic map, and Wang
extended this result to a mean curvature flow in a Euclidean space by proving
its Gauss maps satisfy the harmonic map heat flow equation. In this paper, we
deduce the evolution equation for the Gauss maps of a Ricci-mean curvature
flow, and as a direct corollary we prove that the Gauss maps of a Ricci-mean
curvature flow satisfy the vertically harmonic map heat flow equation when the
codimension of submanifolds is 1.

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph