Oberseminar Differentialgeometrie: Fabian Lehmann (London): Cohomogeneity one families in Spin(7) geometry
Montag, 20.01.2020 16:15 im Raum SR4
Spin(7) is one of the special holonomy groups on Berger's list which gives rise to Ricci flat metrics. The condition that the holonomy of an 8-manifold reduces to Spin(7) gives rise to a complicated system of non-liner PDEs. In the non-compact situation, symmetries can be used to reduce this complexity. As manifolds with special holonomy cannot be homogeneous, the most symmetric case are group actions with cohomogeneity one, i.e. where a generic orbit has codimension one. In this case the PDE system is reduced to an ODE system. I will give an overview of recent progress in the construction of complete cohomogeneity one Spin(7) holonomy metrics. All examples have an asymptotically locally conical (ALC) or asymptotically conical (AC) geometry at infinity.