Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Totally geodesic property of the Hopf vector field   We prove that the Hopf vector field is a unique one among geodesic
covariantly normal unit vector fields on spheres such that the submanifold
generated by the field is totally geodesic in the unit tangent bundle with
Sasaki metric. As application, we give a new proof of stability (instability)
of the Hopf vector field with respect to volume variation using standard
approach from the theory of submanifolds and find exact boundaries for the
sectional curvature of the Hopf vector field.

19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas