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)
A CR manifold consists of a differentiable manifold together with a subbundle of the complexified tangent bundle, such that and .
CR manifold structure are equivalently certain first-order integrable G-structures (Dragomi-Tomassini 06, section 1.6), a type of parabolic geometry.
A close analogy between CR geometry and supergravity superspacetimes (as both being torsion-ful integrable G-structures) is pointed out in (Lott 01 exposition (4.2)).
BR manifold?
The original article is
Surveys:
Howard J. Jacobowitz, An Introduction to CR Structures, Mathematical Surveys and Monographs Volume: 32; (1990) (ISBN:978-0-8218-1533-5, doi:10.1090/surv/032)
Sorin Dragomir, Giuseppe Tomassini, Differential Geometry and Analysis on CR Manifolds, Birkhäuser, 2006 (doi:10.1007/0-8176-4483-0)
See also
Discussion of orbifolds with CR-structure:
Discussion from the point of view of Cartan geometry/parabolic geometry includes
Discussion of spherical CR manifolds locally modeled on the Heisenberg group is in:
Last revised on July 18, 2020 at 18:45:05. See the history of this page for a list of all contributions to it.