A CR manifold is a smooth real manifold 
with a complex subbundle 
of its complexified tangent
bundle satisfying 
and closed under Lie brackets of local sections. Its
complex rank is the CR dimension. The CR codimension is 
.
A real hypersurface in 
inherits a CR structure of dimension 
from the complex tangent directions. A CR function is annihilated
by all local sections of 
.
A local CR embedding into complex Euclidean space is a smooth embedding whose coordinate
functions are CR functions.
An abstract CR structure need not admit such a local embedding. The Trautman conjecture proposed a sufficient condition in real dimension 3 in terms of a nowhere-zero closed canonical form.
