Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz minimality of Hopf fibrations and Hopf vector fields   Given a Hopf fibration of a round sphere by parallel great subspheres, we
prove that the projection map to the base space is, up to isometries of domain
and range, the unique Lipschitz constant minimizer in its homotopy class.
Similarly, given a Hopf fibration of a round sphere by parallel great circles,
we view a unit vector field tangent to the fibres as a cross-section of the
unit tangent bundle of the sphere, and prove that it is, up to isometries of
domain and range, the unique Lipschitz constant minimizer in its homotopy
class. Previous attempts to find a mathematical sense in which Hopf fibrations
and Hopf vector fields are optimal have met with limited success.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th