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)
There are two different meanings of horizontal differential form
Given a bundle of smooth manifolds,
then a differential form on the total space is horizontal if it vanishes on vertical vector fields:
in the context of variational calculus:
a differential form on the the total space of the jet bundle of is horizontal if it is in the horizontal component of the variational bicomplex of .
Last revised on March 6, 2020 at 14:03:30. See the history of this page for a list of all contributions to it.