synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
The metric cone over complex projective 3-space carries the structure of a G₂-manifold whose Riemannian metric is invariant under the canonical Sp(2) action by left-matrix multiplication on homomogeneous coordinates in (Bryant-Salamon 89, see also Acharya-Bryant-Salamon 20).
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)
Bobby Acharya, Robert Bryant, Simon Salamon, A circle quotient of a cone, Differential Geometry and its Applications Volume 73, December 2020, 101681 (arXiv:1910.09518, doi:10.1016/j.difgeo.2020.101681)
As a compactification-space for M-theory on G₂-manifolds:
Last revised on July 18, 2024 at 11:56:00. See the history of this page for a list of all contributions to it.