A circle quotient of a G_2 cone
A study is made of R^6 as a singular quotient of the conical space R^+×CP^3 with holonomy G_2 with respect to an obvious action by U(1) on CP^3 with fixed points. Closed expressions are found for the induced metric, and for both the curvature and symplectic 2-forms characterizing the reduction. All these tensors are invariant by a diagonal action of SO(3) on R^6, which can be used effectively to describe the resulting geometrical features.
Bryant, R; Acharya, B; Salamon, S
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