Search

In this paper, we say that a vector field $$\sigma $$ on a Riemannian manifold $$M$$ is harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on $$TM$$ with respect to which $$\sigma $$ is a harmonic section. If $$M$$ is a simply-connected non-flat space form other than the 2-sphere, examples are obtained of conformal vector fields that are harmonic. In particular, the harmonic Killing fields and conformal gradient fields are classified, a loop of non-congruent harmonic conformal fields on the hyperbolic plane constructed, and the 2-dimensional classification achieved for conformal fields. A classification is then given of all harmonic quadratic gradient fields on spheres. [ABSTRACT FROM AUTHOR]