A construction of Spin(7)-instantons

Author: 

Tanaka, Y

Publication Date: 

12 April 2012

Journal: 

Annals of Global Analysis and Geometry

Last Updated: 

2019-08-18T05:52:19.667+01:00

Issue: 

4

Volume: 

42

DOI: 

10.1007/s10455-012-9324-2

page: 

495-521

abstract: 

Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphic involution fixing only the singular points. On the other hand, there are higher-dimensional analogues of anti-self-dual instantons in four dimensions on Spin(7)-manifolds, which are called Spin(7)-instantons. They are minimizers of the Yang-Mills action, and the Spin(7)-instanton equation together with a gauge fixing condition forms an elliptic system. In this article, we construct Spin(7)-instantons on the examples of compact Spin(7)-manifolds above, starting with Hermitian-Einstein connections on the Calabi-Yau four-orbifolds and ALE spaces. Under some assumptions on the Hermitian-Einstein connections, we glue them together to obtain Spin(7)-instantons on the compact Spin(7)-manifolds. We also give a simple example of our construction. © 2012 Springer Science+Business Media B.V.

Symplectic id: 

366944

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article