Abstract
In this article, we use the pluricomplex Green function to give a sufficient condition for the existence and the completeness of the Bergman metric. As a consequence, we proved that a simply connected complete Kahler manifold possesses a complete Bergman metric provided that the Riemann sectional curvature < -A/ρ 2 , which implies a conjecture of Greene and Wu. Moreover, we obtain a sharp estimate for the Bergman distance on such manifolds.
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