In mathematics, a CR manifold is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge.
Formally, a CR manifold is a differentiable manifold M together with a preferred complex distribution L, or in other words a subbundle of the complexified tangent bundle CTM = TM ⊗ C such that
- (L is formally integrable)
- (L is almost Lagrangian).
The bundle L is called a CR structure on the manifold M.
The abbreviation CR stands for Cauchy-Riemann or Complex-Real.
Read more about CR Manifold: Introduction and Motivation, Abstract CR Structures, Examples
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