Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of Examples of Sacksteder and Bourgain   Finding examples of tangentially degenerate submanifolds (submanifolds with
degenerate Gauss mappings) in an Euclidean space $R^4$ that are noncylindrical
and without singularities is an important problem of differential geometry. The
first example of such a hypersurface was constructed by Sacksteder in 1960. In
1995 Wu published an example of a noncylindrical tangentially degenerate
algebraic hypersurface in $R^4$ whose Gauss mapping is of rank 2 and which is
also without singularities. This example was constructed (but not published) by
Bourgain.
  In this paper, the authors analyze Bourgain's example, prove that, as was the
case for the Sacksteder hypersurface, singular points of the Bourgain
hypersurface are located in the hyperplane at infinity of the space $R^4$, and
these two hypersurfaces are locally equivalent.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga