On pseudo-harmonic maps in conformal geometry

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We discuss existence theorems and obtain an ex-tension of Siu’s strong rigidity to Kähler-Weyl geometry. Other applications include topological obstructions to the existence of Kähler-Weyl structures. For example, we show that no co-compact lattice in SO(1,n), n> 2, can be the fundamental group of a compact Kähler-Weyl manifold. The purpose of this paper is to introduce and study an elliptic quasilinear system of equa-tions on maps between manifolds endowed with linear connections. This system gener-alises the harmonic map equation and, in many situations, is more suitable for geometric applications. We demonstrate this in the context of conformal geometry. More precisely