On some euclidean einstein metrics
Tóm tắt
We prove that the complex manifold of the superposition Eguchi-Hanson metric plus the pseudo-Fubini-Study metric is equal to the total space of the holomorphic line bundle of degree −n on the Riemann sphere. The apparent singularities of the metric can be resolved only if the Eguchi-Hanson parameter satisfies a
4=4(n−2)2(n+1)/3Λ2, n≥3. We give a geometrical explanation of the fact that we need n≥3. Finally, we generalize the metric of Gegenberg and Das to obtain a triaxial vacuum metric.
Tài liệu tham khảo
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