A circle quotient of a G2 cone

Abstract 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 S O ( 3 ) on R 6 , which can be used effectively to describe the resulting geometrical features.