Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: M\"{o}bius structures and Weingarten endomorphisms of spacelike
  submanifolds   Starting from a Riemannian conformal structure on a manifold $M$, we provide
a method to construct a family of Lorentzian manifolds. The construction relies
on the choice of a metric in the conformal class and a smooth $1$-parameter
family of self-adjoint tensor fields and it has been inspired by the Fefferman
and Graham ambient metric for conformal structures. Every metric in the
conformal class corresponds to the induced metric on a codimension two
spacelike submanifold into these Lorentzian manifolds. Under suitable choices
of the $1$-parameter family of tensor fields, there exists a lightlike normal
vector field along such spacelike submanifolds which Weingarten endomorphisms
provide a M\"{o}bius structure on the Riemannian conformal structure.
Conversely, every M\"{o}bius structure on a Riemannian conformal structure
arises in this way. The Ricci-flatness condition along the scale bundle as a
lightlike hypersurface into these Lorentzian manifolds is studied by means of
the initial velocity of the $1$-parameter family of self-adjoint tensor fields.
Finally, flat M\"{o}bius structures are characterized in terms of the extrinsic
geometry of the corresponding spacelike surfaces.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph