On factorization theorems of pluriharmonic maps into the unitary group (Q1364965)

Let \(M\) be a Kähler manifold and let \(X\) be a Riemannian manifold. A smooth map \(\varphi: M\to X\) is pluriharmonic if and only if for any holomorphic curve \(\tau: C \to M\) the composite \(\varphi \circ \tau\) is always harmonic. This property can also be characterized in terms of a differential equation for \(\varphi\). The authors study the case \(X = U(N)\), the unitary group. They essentially show that under a certain finiteness assumption a pluriharmonic map \(\varphi: M\to U(N)\) can be uniquely written as a product of simpler maps, called meromorphic unitons. In the case \(M= \mathbb{C} P^1\), this goes back to [\textit{J. C. Wood}, Proc. Lond. Math. Soc., III. Ser. 58, 608-624 (1989; Zbl 0679.58015)]. A similar result is obtained when \(X\) is a Grassmannian.