Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature conditions for spatial isotropy   In the context of mathematical cosmology, the study of necessary and
sufficient conditions for a semi-Riemannian manifold to be a (generalised)
Robertson-Walker space-time is important. In particular, it is a requirement
for the development of initial data to reproduce or approximate the standard
cosmological model. Usually these conditions involve the Einstein field
equations, which change if one considers alternative theories of gravity or if
the coupling matter fields change. Therefore, the derivation of conditions
which do not depend on the field equations is an advantage. In this work we
present a geometric derivation of such a condition. We require the existence of
a unit vector field to distinguish at each point of space two (non-equal)
sectional curvatures. This is equivalent for the Riemann tensor to adopt a
specific form. Our geometrical approach yields a local isometry between the
space and a Robertson-Walker space of the same dimension, curvature and metric
tensor sign (the dimension of the largest subspace on which the metric tensor
is negative definite). Remarkably, if the space is simply-connected, the
isometry is global. Our result generalises the theorem that spaces of the same
curvature, dimension and metric tensor sign must be locally isometric to a
class of spaces that have non-constant curvature. Because we do not make any
assumptions regarding field equations, matter fields or metric tensor sign, one
can readily use this result to study cosmological models within alternative
theories of gravity or with different matter fields.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs