Harmonic metrics, harmonic tensors, and Gauss maps

Abstract

\S 1. Introduction. If $\phi:(M, g)arrow(N,\tilde{g})$ is a harmonic immersion $($ [4] or Section 3 $)^{r}$ then the identity map $1_{M}$ : $(M, g)arrow(M, \phi^{*}\tilde{g})$ is harmonic (Proposition 3.1). Thus it would be natural to study the Riemannian metrics $G$ such that $1_{M}$ : $(M, g)arrow(M, G)$ is harmonic. We say that $G$ is then a harmonic metric with respect to the given Riemannian metric $g$ . We will study the space $\mathcal{H}_{g}$ of these $G$ in Section 2.