A circle quotient of a $G_2$ cone

Bobby Samir Acharya; Robert L. Bryant; Simon Salamon

A circle quotient of a $G_2$ cone

Differential Geometry 2020-09-01 v2

Authors: Bobby Samir Acharya , Robert L. Bryant , Simon Salamon

Abstract

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.

Keywords

g2 cone circle quotient induced metric curvature form symplectic form so(3) invariance calibrated geometry

Cite

@article{arxiv.1910.09518,
  title  = {A circle quotient of a $G_2$ cone},
  author = {Bobby Samir Acharya and Robert L. Bryant and Simon Salamon},
  journal= {arXiv preprint arXiv:1910.09518},
  year   = {2020}
}

Comments

45 pages, 3 figures. Minor corrections and clarifications, this version accepted for publication in Differential Geometry and its Applications

A circle quotient of a $G_2$ cone

Abstract

Keywords

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