Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real and complex k-planes in convex hypersurfaces   It is shown that that the rank of the second fundamental form (resp. the Levi
form) of a $\mathcal C^2$-smooth convex hypersurface $M$ in $\Bbb R^{n+1}$
(resp. $\Bbb C^{n+1}$) does not exceed an integer constant $k<n$ near a point
$p\in M,$ then through any point $q\in M$ near $p$ there exists a real (resp.
complex) $(n-k)$-dimensional plane that locally lies on $M.$

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an