Solenoidal unit vector fields with minimum energy

SALVAI, MARCOS; BRITO, FABIANO

OSAKA JOURNAL OF MATHEMATICS

OSAKA JOURNAL OF MATHEMATICS

Año: 2004 vol. 41 p. 533 - 544

0030-6126

In this article we give examples of compact manifolds P admitting homogeneous Riemannian metrics (depending on a real parameter) and unit vector fields V , which are critical for the total bending functional and have minimum energy among all solenoidal (that is, divergence free) unit vector fields. The family of manifolds P, introduced by Gary Jensen to provide new examples of Einstein metrics, consists of total spaces of principal bundles over symmetric spaces, and includes for instance Berger spheres. Those of Jensen's examples involving classical groups (and one exceptional) are made explicit for instance as Grassmann- or Stiefel-like manifolds.