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- W1566295864 abstract "The Taub-NUT metrics were found by Taub [10] in 1951, and extended by Newmann-Unti-Tamburino [8] in 1963. They are Ricci-flat self-dual metrics on R and were given by Hawking [4] as a non-trivial example of the gravitational instantons which he advocated in 1977. Iwai-Katayama [5] generalized the Taub-NUT metrics in the following way. Suppose that a metric g on an open interval U in (0, +°°) and a family of Berger metrics g(r) on S indexed by U are given, where a Berger metric is by definition a right invariant metric on S = Sp(ϊ) which is further left £/(l)-invariant. Then the twisted product g=g + g(r) on the annulus £/xSC/f{0} is called a generalized Taub-NUT metric. In [5] they explicitly wrote out the conformally flat ones among those metrics and gave a condition for a generalized Taub-NUT metric to be self-dual in terms of a certain ordinary differential equation. In this paper we will solve this differential equation and explicitly express all the self-dual generalized Taub-NUT metrics. As an application we get a family of complete Einstein self-dual generalized Taub-NUT metrics on 4-balls. This reproduces the Einstein self-dual metrics found by Pedersen [9] which have Berger spheres as conformal infinities." @default.
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- W1566295864 date "1995-09-01" @default.
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- W1566295864 title "Self-dual generalized Taub-NUT metrics" @default.
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- W1566295864 doi "https://doi.org/10.18910/12566" @default.
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