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In mathematics, a CR manifold, or Cauchy–Riemann 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 complex subbundle of the complexified tangent bundle C T M = T M ⊗ R C {\displaystyle \mathbb {C} TM=TM\otimes _{\mathbb {R} }\mathbb {C} } such that
The subbundle L is called a CR structure on the manifold M.
The abbreviation CR stands for "Cauchy–Riemann" or "Complex-Real".