S. Salamon

New Inhomogeneous Nearly $\mathrm{G}_2$-metric on the Berger Space and a Sine Cone Desingularisation

Nearly $\mathrm{G}_2$ manifolds are positive Einstein seven-dimensional manifolds whose associated cone metric has special holonomy equal to, or contained in, $\mathrm{Spin}(7)$. We study nearly parallel $\mathrm{G}_2$-structures invariant under a cohomogeneity-one action of $\mathrm{SO}(4)$, and construct the first in...