tt*-geometry and pluriharmonic maps

Lars Schaefer (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 Rheinische Friedrich-Wilhelms-Universität Bonn

In this paper we use the real differential geometric definition of a metric (an unimodular oriented metric) tt*-bundle of Cortés and the author 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.

Mots clés: tt*-geometry and tt*-bundles; pluriharmonic maps; pseudo-Riemannian symmetric spaces

Domaines: Géométrie différentielle [math.DG]

Lars Schaefer. tt*-geometry and pluriharmonic maps. Annals of Global Analysis and Geometry, 2005, 28 (3), pp.285-300. ⟨10.1007/s10455-005-7947-2⟩. ⟨hal-00143285⟩