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A positively curved compact Kahler manifold has second Betti number equal to 1 by a result of Bishop and Goldberg. So as Torsten Ekedahl commented, the only sphere that admits a Kahler structure is a 2-sphere.

And as Donu Arapura commented, a discussion of the classification of Kahler structures is herehere. For another discussion, see herehere.

A positively curved compact Kahler manifold has second Betti number equal to 1 by a result of Bishop and Goldberg. So as Torsten Ekedahl commented, the only sphere that admits a Kahler structure is a 2-sphere.

And as Donu Arapura commented, a discussion of the classification of Kahler structures is here. For another discussion, see here.

A positively curved compact Kahler manifold has second Betti number equal to 1 by a result of Bishop and Goldberg. So as Torsten Ekedahl commented, the only sphere that admits a Kahler structure is a 2-sphere.

And as Donu Arapura commented, a discussion of the classification of Kahler structures is here. For another discussion, see here.

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Sean Lawton
Sean Lawton
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A positively curved compact Kahler manifold has second Betti number equal to 1 by a result of Bishop and Goldberg. So as Torsten Ekedahl commented, the only sphere that admits a Kahler structure is a 2-sphere.

And as Donu Arapura commented, a discussion of the classification of Kahler structures is here. For another discussion, see here.