A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres

Xuwen Zhu

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arXiv · 2407.20149

A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres

Xuwen Zhu

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Abstract

This note extends the construction of $D_{k}$ ALF gravitational instantons in Schroers--Singer to a new case where the nonlinear superposition is given by the $D_{1}$ Atiyah--Hitchin metric and $k-1$ copies of $A_{0}$ Taub-NUT metrics. We then give a general class of ALF spaces such that each of them contains a non-holomorphic minimal sphere. Together with Foscolo's construction this gives a large class of $K3$ surfaces containing non-holomorphic minimal spheres.

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Xuwen Zhu. 2024-07-29. A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres. https://arxiv.org/abs/2407.20149

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