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Conformal completion of $$\mathbb{U}(n)$$-invariant Ricci-flat Kähler metrics at infinity. (English) Zbl 0870.53040
In a recent paper [Lett. Math. Phys. 38, 411-419 (1996; Zbl 0860.53029)], the authors exhibited the first example of a Riemannian spin manifold of $$m=4$$ dimensions which is not conformally flat and which admits twistor spinors with zeros. It was then shown that under a conformal change, a pair of linearly independent parallel spinors of the Eguchi-Hanson metric become twistor spinors with zeros at infinity.
The present investigation is intended to extend this result to $$m=2n$$ dimensions, $$n\geq 2$$, for a $$U(n)$$-invariant cohomogenity one metric which is not conformally flat, and admits twistor spinors with zeros. Their construction makes use of previously known results of E. Calabi, D. Z. Freedman and G. W. Gibbons on the conformal completion of $$U(n)$$-invariant metrics as described in the title of the paper. Presumably this work has implications for the theory of gravitational instantons; however, these are not discussed in the present paper.

##### MSC:
 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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##### References:
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