Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structures

Víctor Manero

Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structures

Differential Geometry 2018-03-13 v3

Authors: Víctor Manero

Abstract

We describe a method to obtain $\mathrm{SU}(3)$ -structures and $\mathrm{G}_2$ -structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ -structures, on 5 and 6-dimensional manifolds whose induced metric is Einstein can produce, via warped products, different classes $\mathrm{SU}(3)$ and $\mathrm{G}_2$ -structures such that its associated metric is also Einstein.

Keywords

einstein metrics metric spaces holonomy

Cite

@article{arxiv.1607.07775,
  title  = {Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structures},
  author = {Víctor Manero},
  journal= {arXiv preprint arXiv:1607.07775},
  year   = {2018}
}

Comments

The paper has been deeply modified and improved in a current collaboration, so almost all the contents have been changed and an author has been added in a newest version

Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structures

Abstract

Keywords

Cite

Comments

Related papers