Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New examples of Willmore submanifolds in the unit sphere via
  isoparametric functions,II   This paper is a continuation of a paper with the same title of the last two
authors. In the first part of the present paper, we give a unified geometric
proof that both focal submanifolds of every isoparametric hypersurface in
spheres with four distinct principal curvatures are Willmore. In the second
part, we completely determine which focal submanifolds are Einstein except one
case.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th