  We study harmonic maps from Riemannian manifolds into arbitrary
non-positively curved and CAT(-1) metric spaces. First we discuss the domain
variation formula with special emphasis on the error terms. Expanding higher
order terms of this and other formulas in terms of curvature, we prove an
analogue of the Eels-Sampson Bochner formula in this more general setting. In
particular, we show that harmonic maps from spaces of non-negative Ricci
curvature into non-positively curved spaces have subharmonic energy density.
When the domain is compact the energy density is constant, and if the domain
has a point of positive Ricci curvature every harmonic map into an NPC space
must be constant.
