tt*-geometry and pluriharmonic maps

In this paper we use the real differential geometric definition of a metric ( a unimodular oriented metric) tt*-bundle of Cortes and the author (Topological-anti-topological fusion equations, pluriharmonic maps and special Kahler manifolds) to define a map Phi from the space of metric ( unimodular oriented metric) tt*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to GL( r)/ O(p, q) ( respectively SL(r)/SO(p, q)), where (p, q) is the signature of the metric. In the sequel the image of the map Phi is characterized. It follows, that in signature (r, 0) the image of Phi is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin ( Comm. Math. Phys. 152 ( 1992; S539 - S564).