Degeneration of ALF D_n Metrics
G. Chalmers, M. Rocek, S. Wiles
TL;DR
This paper investigates the degeneration of ALF D_n hyperk"ahler metrics, showing how they limit to multi-Taub-NUT metrics as certain parameters vanish, using Legendre transform techniques.
Contribution
It provides a detailed analysis of the degeneration process of ALF D_n metrics to multi-Taub-NUT metrics via constraint equations derived from Legendre transforms.
Findings
The constraint equation enforces the metric's limit to multi-Taub-NUT.
Behavior of the ALF D_n metrics under parameter degeneration is characterized.
The analysis connects ALF D_n metrics with well-known multi-Taub-NUT geometry.
Abstract
Beginning with the Legendre transform construction of hyperk\"ahler metrics, we analyze the ALF version of the D_n metrics. We determine the constraint equation obtained from extremizing the coordinate of the generating function F(z,\bar{z},u,\bar{u},w) and study its behavior as we send two of the mass parameters of the 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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