Abstract:

Given a Riemannian manifold (M,g), a natural object to consider is its associated metric cone M x R^+, dr^2+r^2 g_M). The geometric properties of the cone can then be rephrased in terms of properties of M itself, which can be then used to define new (or rediscover) geometries on M. In my talk, I will explore this question from the perspective of special holonomy and describe the associated special geometries.