On the energy of unit vector fields with isolated singularities

Volume 73 / 2000

Fabiano Brito, Paweł Walczak Annales Polonici Mathematici 73 (2000), 269-274 DOI: 10.4064/ap-73-3-269-274


We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').


  • Fabiano Brito
  • Paweł Walczak

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