CR manifold
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 [ L , L ] ⊆ L {\displaystyle [L,L]\subseteq L} (L is formally integrable) L ∩ L ¯ = { 0 } {\displaystyle L\cap {\bar {L}}=\{0\}} .