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

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

2010-01-11

arxiv.org/abs/1001.1622v3

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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