Some geometrical properties of Berger Spheres

Abstract

Our aim in this paper is to investigate some geometrical properties of Berger Spheres i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector fields. We determine all vector fields which are critical points for the energy functional restricted to vector fields. We also see that do not exist any vector fields defining harmonic map, and the energy of critical points is explicitly calculated.