Geometric Transitions with Spin(7) Holonomy via a Dynamical System

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 transition in setting Calabi–Yau 3-folds. Furthermore, we discover that there is another have similar asymptotic behaviour on end, but are other end. obtain our results relating Spin(7)-equations simple dynamical system 3-dimensional cube.