nLab G₂-conifold

Idea

A G₂-manifold with conical singularities is also called a $G_2$-conifold.

References

$G_2$-conifolds

On G₂-conifolds (G₂-manifolds with conical singularities):

Survey:

• Spiro Karigiannis, $G_2$-conifolds: A survey, 2014 (pdf)

• Mark Haskins, Exotic Einstein metrics on $S^6$ and $S^3 \times S^3$ nearly Kähler 6-manifolds and $G_2$-holonomy cones, 2016 (pdf)

Three simply connected $G_2$-cones are known: the

1. metric cone on complex projective 3-space

2. metric cone on $S^3 \times S^3$

3. metric cone on $SU(3) / (U(1) \times U(1))$

• Robert Bryant, Simon Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J. Volume 58, Number 3 (1989), 829-850 (euclid:euclid.dmj/1077307681)

• Gary Gibbons, Don Page, Christopher Pope, Einstein metrics on $S^3$, $\mathbb{R}^3$ and $\mathbb{R}^4$ bundles, Comm. Math. Phys. Volume 127, Number 3 (1990), 529-553 (euclid:cmp/1104180218)

More on the metric cone over complex projective 3-space as a G₂-manifold:

• Bobby Acharya, Robert Bryant, Simon Salamon, A circle quotient of a $G_2$ cone, Differential Geometry and its Applications Volume 73, December 2020, 101681 (arXiv:1910.09518, doi:10.1016/j.difgeo.2020.101681)