On the Critical Points of the E_k Functionals in Kahler Geometry

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We prove that a Kahler metric in the anticanonical class which is a critical point of the functional E_k and has nonnegative Ricci curvature, is necessarily Kahler-Einstein. This partially answers a question of X.X.Chen.
4 pages; minor changes; final version to appear in Proc. AMS

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