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Remarks on the existence of bilaterally symmetric extremal Kahler metrics on $mathbb{CP}^2sharp 2bar{mathbb{CP}^2}$

104   0   0.0 ( 0 )
 Added by Weiyong He
 Publication date 2007
  fields
and research's language is English
 Authors Weiyong He




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In this short note we show that the existence of bilaterally symmetric extremal Kahler metrics on $mathbb{CP}^2sharp 2bar{mathbb{CP}^2}$.



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In this article, we show the existence of a nontrivial Riemann surface lamination embedded in $mathbb{CP}^2$ by using Donaldsons construction of asymptotically holomorphic submanifolds. Further, the lamination we obtain has the property that each leaf is a totally geodesic submanifold of $mathbb{CP}^2 $ with respect to the Fubini-Study metric. This may constitute a step in understanding the conjecture on the existence of minimal exceptional sets in $mathbb{CP}^2$.
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