Einstein Metrics on Complex Surfaces

Details Einstein Metrics on Complex Surfaces Einstein Metrics on Complex Surfaces

1995-06-29

arxiv.org/abs/dg-ga/9506012v1

Mathematics

Differential Geometry

latex, 2 figures

Scientific paper

We consider compact complex surfaces with Hermitian metrics which are
Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at
1,2, or 3 points, and the isometry group of the metric must contain a 2-torus.
Thus the Page metric on CP2#(-CP2) is almost the only metric of this type.

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