Communications in Analysis and Geometry

Volume 30 (2022)

Number 7

Generalized Kähler Taub-NUT metrics and two exceptional instantons

Pages: 1575 – 1632

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n7.a5

Author

Brian Weber (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Abstract

We study the one-parameter family of generalized Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extent that should be sufficient for blow-up and gluing arguments. In particular we parameterize their geodesics from the origin, determine curvature fall-off rates and volume growth rates for metric balls, and find blow-down limits.

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Received 14 August 2017

Accepted 27 December 2019

Published 25 May 2023