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 S4 that retain invariance under the action of Sp(2), showing that the metrics obtained in this way are isometric.
Conti, D., Perolini, D. (2021). Linear perturbations of metrics with holonomy Spin(7). DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 78 [10.1016/j.difgeo.2021.101792].
Linear perturbations of metrics with holonomy Spin(7)
Conti, Diego
;Perolini, Daniel
2021
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 S4 that retain invariance under the action of Sp(2), showing that the metrics obtained in this way are isometric.
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