Abstract
Building on Donaldson’s work on constant scalar curvature metrics, we study the space of regular Kahler metrics Eω, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Sects. 2 and 3 a review of Donaldson’s moment map approach, we study the ‘‘essential’’ uniqueness of balanced basis (i.e. of coherent states) in a more general setting (Theorem 2.5). We then study the space Eω in Sect.4 and we show in Sect.5 how all the tools needed can be defined also in the case of non-compact manifolds.
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