Equivariant Kählerian extensions of contact manifolds
For contact manifolds $(M, η)$ a complexification $M^c$ is constructed to which the contact form $η$ extends such that the exterior derivative of the extended form is Kählerian. In the case of a proper action of an extendable Lie group this construction is realized in an equivariant way. In a simultaneous stratification of $M$ and $M^c$ according to the istropy type, it is shown that the Kählerian reduction of the complexification can be seen as the complexification of the contact reduction.
math.CV↗