Degeneration of ALF Dn Metrics
Abstract
Beginning with the Legendre transform construction of hyperk\"ahler metrics, we analyze the ALF version of the Dn metrics. We determine the constraint equation obtained from extremizing the w coordinate of the generating function F(z,z,u,u,w) and study its behavior as we send two of the mass parameters of the Dn metric to zero. We find that the constraint equation enforces the limit that the metric becomes that of multi-Taub-NUT.
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