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Zeitschrift für Analysis und ihre Anwendungen

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Volume 16, Issue 1, 1997, pp. 113–117
DOI: 10.4171/ZAA/753

Published online: 1997-03-31

Conformal Completion of $\mathbb U(n)$-invariant Ricci-Flat Kãhler Metrics at Infinity

Wolfgang Kühnel[1] and Hans-Bert Rademacher[2]

(1) Universität Stuttgart, Germany
(2) Universität Leipzig, Germany

For every $n≥2$ we give an example of a complete $\mathbb U(n)$-invariant cohomogeneity one metric on $\mathbb R^{2n}$ which is not conformally flat and which carries twistor spinors with zeros. The construction uses a conformal completion at infinity of a $\mathbb U(n)$-invariant Ricci-flat Kähler metric on $\mathbb R^{2n} \backslash \lbrace 0 \rbrace$ given by Calabi [2] and by Freedman and Gibbons [4]. This extends our results in [6) for $n = 2$ to all even dimensions.

Keywords: Ricci-flat Kähler metrics, conformal completion, twistor spinor, cohomogeneity one metric, asymptotic locally Euclidean metric

Kühnel Wolfgang, Rademacher Hans-Bert: Conformal Completion of $\mathbb U(n)$-invariant Ricci-Flat Kãhler Metrics at Infinity. Z. Anal. Anwend. 16 (1997), 113-117. doi: 10.4171/ZAA/753