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On the critical points of the  functionals in Kähler geometry
Author(s):
Valentino
Tosatti
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3985-3988.
MSC (2000):
Primary 32Q20, 58E11
Posted:
September 12, 2007
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Abstract:
We prove that a Kähler metric in the anticanonical class, that is a critical point of the functional  and has nonnegative Ricci curvature, is necessarily Kähler-Einstein. This partially answers a question of X.X. Chen.
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Additional Information:
Valentino
Tosatti
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, Massachusetts 02138
Email:
tosatti@math.harvard.edu
DOI:
10.1090/S0002-9939-07-08962-9
PII:
S 0002-9939(07)08962-9
Received by editor(s):
May 8, 2006
Received by editor(s) in revised form:
October 2, 2006
Posted:
September 12, 2007
Additional Notes:
The author is supported by a Harvard Mathematics Department grant
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Haozhao Li, A New Formula for the Energy Functionals Ek and its Applications, International Mathematical Research Notices 2007 (2007), article ID rnm033, 17 pages.
Haozhao Li, On the lower bound of the $K$-energy and $F$-functional, Osaka Journal of Mathematics 45 (2008), 253-264.
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