English

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

Differential Geometry 2015-05-14 v3

Abstract

We completely explore the system of ODE's which is equivalent to the existence of a parallel Spin(7)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.

Keywords

Cite

@article{arxiv.1001.1622,
  title  = {The $Spin(7)$-structures on complex line bundles and explicit Riemannian metrics with SU(4)-holonomy},
  author = {Ya. V. Bazaikin and E. G. Malkovich},
  journal= {arXiv preprint arXiv:1001.1622},
  year   = {2015}
}

Comments

11 pages