On the critical points of the $E_k$ functionals in Kähler geometry
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Abstract:
We prove that a Kähler metric in the anticanonical class, that is a critical point of the functional $E_k$ and has nonnegative Ricci curvature, is necessarily Kähler-Einstein. This partially answers a question of X.X. Chen.References
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Additional Information
- Valentino Tosatti
- Affiliation: Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, Massachusetts 02138
- MR Author ID: 822462
- Email: tosatti@math.harvard.edu
- Received by editor(s): May 8, 2006
- Received by editor(s) in revised form: October 2, 2006
- Published electronically: September 12, 2007
- Additional Notes: The author is supported by a Harvard Mathematics Department grant
- Communicated by: Richard A. Wentworth
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3985-3988
- MSC (2000): Primary 32Q20, 58E11
- DOI: https://doi.org/10.1090/S0002-9939-07-08962-9
- MathSciNet review: 2341949