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

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.

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