Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biharmonic hypersurfaces in a Riemannian manifold with non-positive
  Ricci curvature   In this paper, we show that, for a biharmonic hypersurface $(M,g)$ of a
Riemannian manifold $(N,h)$ of non-positive Ricci curvature, if $\int_M|H|^2
v_g<\infty$, where $H$ is the mean curvature of $(M,g)$ in $(N,h)$, then
$(M,g)$ is minimal in $(N,h)$. Thus, for a counter example $(M,g)$ in the case
of hypersurfaces to the generalized Chen's conjecture (cf. Sect.1), it holds
that $\int_M|H|^2 v_g=\infty$.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys