Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equiaffine Darboux Frames for Codimension 2 Submanifolds contained in
  Hypersurfaces   Consider a codimension $1$ submanifold $N^n\subset M^{n+1}$, where
$M^{n+1}\subset\mathbb{R}^{n+2}$ is a hypersurface. The envelope of tangent
spaces of $M$ along $N$ generalizes the concept of tangent developable surface
of a surface along a curve. In this paper, we study the singularities of these
envelopes.
  There are some important examples of submanifolds that admit a vector field
tangent to $M$ and transversal to $N$ whose derivative in any direction of $N$
is contained in $N$. When this is the case, one can construct transversal plane
bundles and affine metrics on $N$ with the desirable properties of being
equiaffine and apolar. Moreover, this transversal bundle coincides with the
classical notion of Transon plane. But we also give an explicit example of a
submanifold that do not admit a vector field with the above property.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat