Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A conformal integral invariant on Riemannian foliations   Let $M$ be a closed manifold which admits a foliation structure $\mathcal{F}$
of codimension $q\geq 2$ and a bundle-like metric $g_0$. Let $[g_0]_B$ be the
space of bundle-like metrics which differ from $g_0$ only along the horizontal
directions by a multiple of a positive basic function. Assume $Y$ is a
transverse conformal vector field and the mean curvature of the leaves of
$(M,\mathcal{F},g_0)$ vanishes. We show that the integral
$\int_MY(R^T_{g^T})d\mu_g$ is independent of the choice of $g\in [g_0]_B$,
where $g^T$ is the transverse metric induced by $g$ and $R^T$ is the transverse
scalar curvature. Moreover if $q\geq 3$, we have $\int_MY(R^T_{g^T})d\mu_g=0$
for any $g\in [g_0]_B$. However there exist codimension 2 minimal Riemannian
foliations $(M,\mathcal{F},g)$ and transverse conformal vector fields $Y$ such
that $\int_MY(R^T_{g^T})d\mu_g\neq 0$. Therefore, it is a nontrivial
obstruction for the transverse Yamabe problem on minimal Riemannian foliation
of codimension 2.

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The categories of this paper are: funct-an
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph