Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
A unit vector field \(X\) on a closed Riemannian manifold \(M\) can be viewed as a map of \(M\) into the unit tangent bundle \(T^1 M\). Since the metric on \(M\) induces a metric on \(T^1 M\), one can look for such vector fields which minimise the energy. The authors show that under some additional curvature condition, unit Killing vector fields on closed 3-manifolds have this property. This leads to examples on quotients of unimodular 3-dimensional Lie groups.
harmonic sections of the unit tangent bundle
scientific article; zbMATH DE number 1780872