Gap properties of harmonic maps and submanifolds

Qun Chen; Zhen Rong Zhou

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We produce new examples of harmonic maps, having as source manifold a space $(M, g)$ of constant curvature and as target manifold its tangent bundle $T M$ , equipped with a suitable Riemannian $g$ -natural metric. In particular, we determine a family of Riemannian $g$ -natural metrics $G$ on $T 𝕊^{2}$ , with respect to which all conformal gradient vector fields define harmonic maps from $𝕊^{2}$ into $(T 𝕊^{2}, G)$ .