On the volume and energy on sections of a circle bundle over a compact Lie group

SALVAI, MARCOS

Valencia

Congreso; International Meeting on Differential Geometry, 6Oth birthday of A. Naveira.; 2001

Let G be a compact simply connected semisimple Lie group endowed with a bi-invariant Riemannian metric and let E -> G be a vector bundle with two- dimensional fibers and a G-invariant metric connection (generically, it has no parallel unit sections). We prove that if E carries the Sasaki metric, then the constant unit sections are exactly those of minimum volume and minimum energy among all smooth sections of the associated circle bundle.