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

Simon Salamon, Ragini Singhal

Nearly ${\mathrm{G}}_2$ manifolds are positive Einstein seven-dimensional manifolds whose associated cone metric has special holonomy equal to, or contained in, $\mathrm{Spin}(7)$. W…