Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypersurfaces of the homogeneous nearly K\"ahler $\mathbb{S}^6$ and
  $\mathbb{S}^3\times\mathbb{S}^3$ with anticommutative structure tensors   Each hypersurface of a nearly K\"ahler manifold is naturally equipped with
two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the
induced almost contact structure $\phi$. In this paper, we show that, in the
homogeneous NK $\mathbb{S}^6$ a hypersurface satisfies the condition
$A\phi+\phi A=0$ if and only if it is totally geodesic; moreover, similar as
for the non-flat complex space forms, the homogeneous nearly K\"ahler manifold
$\mathbb{S}^3\times\mathbb{S}^3$ does not admit a hypersurface that satisfies
the condition $A\phi+\phi A=0$.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas