Unit vector fields on real space forms which are harmonic maps

Abstract

Gs), where e Gs is the Sasaki metric. In this paper, by using a different method, we get an analogue of Han and Yim’s theorem for a Riemannian three-manifold with constant sectional curvature k 6= 0. An immediate consequence is that there does not exist a unit vector field on the hyperbolic three-space that defines a harmonic map. We also extend this result for Riemannian (2n +1)-manifolds (M, g) of constant sectional curvature k > 0 with 1(M) 6= 0.