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Bibliographic Details
Main Author: Zhu, Xuwen
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.20149
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author Zhu, Xuwen
author_facet Zhu, Xuwen
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_20149
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres
Zhu, Xuwen
Differential Geometry
Mathematical Physics
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.
title A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres
topic Differential Geometry
Mathematical Physics
url https://arxiv.org/abs/2407.20149