cr 223

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

[L,L]\subseteq L
(L is formally integrable)



L
∩



L
¯



=
{
0
}

L\cap {\bar {L}}=\{0\}
.The subbundle L is called a CR structure on the manifold M.
The abbreviation CR stands for "Cauchy–Riemann" or "Complex-Real".

View More On Wikipedia.org