Browsing by Author "Salamon, Simon"

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    A circle quotient of a $G_2$ cone
    Acharya, Bobby Samir; Bryant, Robert L; Salamon, Simon
    A study is made of $R^6$ as a singular quotient of the conical space $R^+\times CP^3$ 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.
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    ItemOpen Access
    A circle quotient of a G2 cone
    (Differential Geometry and its Application, 2020-12-01) Bryant, Robert; Acharya, Bobby; Salamon, Simon
    © 2020 A study is made of R6 as a singular quotient of the conical space R+×CP3 with holonomy G2, with respect to an obvious action by U(1) on CP3 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 R6, which can be used effectively to describe the resulting geometrical features.