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Compact extremal versus compact Einstein metrics

Thierry Chave and Galliano Valent

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Using appropriate non-holomorphic coordinates we give an explicit form for Calabi's extremal metrics. Several particular cases of these metrics appear to have been studied later on in the literature. In the four-dimensional case we show, by giving the explicit change in coordinates, that one compact bolt - bolt extremal metric is conformal to Page's compact Einstein metric.


PACS

02.40.-k Geometry, differential geometry, and topology

MSC

58E11 Critical metrics

Subjects

Mathematical physics

Dates

Issue 8 (August 1996)

Received 14 December 1995, in final form 14 June 1996



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