Generalized Kahler Taub-NUTs and Two Exceptional Instantons
Brian Weber
TL;DR
This paper analyzes a family of twisted Kahler Taub-NUT metrics and two exceptional instantons, providing detailed geometric properties to facilitate advanced geometric analysis techniques like blow-up and gluing.
Contribution
It offers a comprehensive parametrization, curvature decay, volume growth, and blow-down limits for these metrics and instantons, aiding future geometric analysis.
Findings
Explicit geodesic parametrization from the origin
Determined curvature decay rates
Established volume growth and blow-down limits
Abstract
We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curvature fall-off rates, volume growth rates for metric balls, and find blow-down limits.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory