The $Spin(7)$-structures on complex line bundles and explicit Riemannian metrics with SU(4)-holonomy

Abstract

We completely explore the system of ODE's which is equivalent to the existence of a parallel $Spin(7)$-structure on the cone over a 7-dimensional 3-Sasakian manifold. The one-dimensional family of solutions of this system is constructed. The solutions of this family correspond to metrics with holonomy SU(4) which generalize the Calabi metrics.

11 pages

Cited by in corpus (2)

• Asymptotically conical Calabi-Yau manifolds, I
• Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces