Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On special types of minimal and totally geodesic unit vector fields   We present a new equation with respect to a unit vector field on Riemannian
manifold $M^n$ such that its solution defines a totally geodesic submanifold in
the unit tangent bundle with Sasaki metric and apply it to some classes of unit
vector fields. We introduce a class of covariantly normal unit vector fields
and prove that within this class the Hopf vector field is a unique global one
with totally geodesic property. For the wider class of geodesic unit vector
fields on a sphere we give a new necessary and sufficient condition to generate
a totally geodesic submanifold in $T_1S^n$.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics