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On the Critical Points of the E_k Functionals in Kahler Geometry

Valentino Tosatti

Published 2005-06-01, updated 2006-10-02Version 2

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.

Comments: 4 pages; minor changes; final version to appear in Proc. AMS
Journal: Proc. Amer. Math. Soc. 135 (2007), no.12, 3985--3988.
Categories: math.DG
Subjects: 32Q20, 58E11
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