Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fiberwise homogeneous fibrations of the 3-dimensional space forms by
  geodesics   A fibration of a Riemannian manifold is fiberwise homogeneous if there are
isometries of the manifold onto itself, taking any given fiber to any other
one, and preserving fibers. Examples are fibrations of Euclidean n-space by
parallel n-planes, and the Hopf fibrations of the round n-sphere by great
n-spheres. In this paper, we describe all the fiberwise homogeneous fibrations
of Euclidean and hyperbolic 3-space by geodesics. Our main result is that, up
to fiber-preserving isometries, there is precisely a one-parameter family of
such fibrations of Euclidean 3-space, and a two-parameter family in hyperbolic
3-space. By contrast, we show in another paper that the only fiberwise
homogeneous fibrations of the round 3-sphere by geodesics (great circles) are
the Hopf fibrations. More generally, we show in that same paper that the Hopf
fibrations in all dimensions are characterized, among fibrations of round
spheres by smooth subspheres, by their fiberwise homogeneity.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat