We clarify the global geometry of two 1-parameter families cohomogeneity one Spin(7) holonomy metrics with generic orbit Aloff–Wallach space $$N(1,-1) \cong \text {SU}(3)/\text {U}(1)$$ and singular orbits $$S^5$$ $${\mathbb {C}}P^{2}$$ , which at short distance were shown to exist by Reidegeld. The fit into geography previously known exceptional provide a analogue well-known conifold transitio...

A Kähler metric is said to be Bochner-Kähler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain well-defined sense, the space of Bochner-Kähler metrics in complex dimension n has real dimension n+1 and a recipe for an explicit formula for any Bochner-Kähler met...

We consider a rank one group G = ? A , B stretch...

A bstract We analyze the perturbative quantization of spectral action in noncommutative geometry and establish its one-loop renormalizability a generalized sense, while staying within framework geometry. Our result is based on expansion terms higher Yang-Mills Chern-Simons forms. In spirit random geometries, we consider path integral over matrix fluctuations around fixed gauge background show t...