  We prove results on solvability of nonlinear elliptic partial differential
systems of principle type of second order. They are consequences of existence
of non-radial solutions for nonlinear partial differential systems of Poisson
type. As applications to geometry, we prove the exsitence of local harmonic
maps with given tangent plane at a point between any Riemannan manifolds. More
generally geometric objects defined by Beltrami-Laplace always exist locally.
