Linear perturbations of metrics with holonomy Spin(7)

Abstract

We apply the method of linear perturbations to the case of Spin(7)-structures, showing that the only nontrivial perturbations are those determined by a rank one nilpotent matrix. We consider linear perturbations of the Bryant-Salamon metric on the spin bundle over $S^4$ that retain invariance under the action of Sp(2), showing that the metrics obtained in this way are isometric.

13 pages

References in corpus (2)

• Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds