Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of the conjugate locus of a general point on ellipsoids
  and certain Liouville manifolds   It is well known since Jacobi that the geodesic flow of the ellipsoid is
"completely integrable", which means that the geodesic orbits are described in
a certain explicit way. However, it does not directly indicate that any global
behavior of the geodesics becomes easy to see. In fact, it happened quite
recently that a proof for the statement "The conjugate locus of a general point
in two-dimensional ellipsoid has just four cusps" in Jacobi's Vorlesungen
\"uber dynamik appeared in the literature. In this paper, we consider Liouville
manifolds, a certain class of Riemannian manifolds which contains ellipsoids.
We solve the geodesic equations; investigate the behavior of the Jacobi fields,
especially the positions of the zeros; and clarify the structure of the
conjugate locus of a general point. In particular, we show that the
singularities arising in the conjugate loci are only cuspidal edges and $D_4^+$
Lagrangian singularities, which would be the higher dimensional counterpart of
Jacobi's statement.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol