On some euclidean einstein metrics

H. Pedersen; B. Nielsen

doi:10.1007/BF00402660

On some euclidean einstein metrics

H. Pedersen^*, B. Nielsen

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

5 Citations (Scopus)

Abstract

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 a⁴=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.

Original language	English
Journal	Letters in Mathematical Physics
Volume	12
Issue number	4
Pages (from-to)	277-282
Number of pages	6
ISSN	0377-9017
DOIs	https://doi.org/10.1007/BF00402660
Publication status	Published - Nov 1986
Externally published	Yes

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abstract = "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 a4=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.",

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AU - Nielsen, B.

PY - 1986/11

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AB - 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 a4=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.

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JO - Letters in Mathematical Physics

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IS - 4

ER -

On some euclidean einstein metrics

Abstract

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