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)
On the Cartesian space the associative 3-form is the differential 3-form which is constant and whose value at the origin on three vectors is
where
is the canonical bilinear form on ;
is the cross product in .
This are the structure constants of the unit octonions.
The Hodge dual of the associative 3-form is sometimes called the co-associative 4-form.
The group of linear diffeomorphisms of which preserve this form is the exceptional Lie group G₂.
classification of special holonomy manifolds by Berger's theorem:
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Last revised on July 18, 2024 at 11:31:27. See the history of this page for a list of all contributions to it.