Principal mappings of 3-dimensional Riemannian spaces into spaces of constant curvature (Q674842)

According to Gauss and others, every 2-dimensional Riemannian manifold can locally be mapped conformally into Euclidean plane. The author looks for analogous results in three dimensions admitting any real space form as target manifold and replacing confomal transformations by harmonic maps which in addition map the orthonormal frame of eigenvectors of the Ricci tensor into an orthogonal frame. In some special examples such maps are constructed explicitly; their local existence is proved in the case where the original Riemannian metric only differs slightly from the Euclidean one.