Ricci flow on KaehlerEinstein surfaces
Abstract
In this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci flow. Moreover, if the initial metric has nonnegative bisectional curvature, using Tian's inequality, we can prove that each of the functionals has uniform lower bound along the flow which gives a set of integral estimates on curvature. Using this set of integral estimates, we are able to show the following theorem: Let M be a KaehlerEinstein surface with positive scalar curvature. If the initial metric has nonnegative sectional curvature and positive somewhere, then the KaehlerRicci flow converges exponentially fast to a KaehlerEinstein metric with constant bisectional curvature.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2000
 arXiv:
 arXiv:math/0010008
 Bibcode:
 2000math.....10008C
 Keywords:

 Differential Geometry
 EPrint:
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