A Kähler structure for the $\mathrm{PU}(2,1)$ configuration space of four points in $S^3$

Abstract

We show that an open subset ${\mathfrak{F}}_4^{\prime \prime }$ of the $\mathrm{PU}(2,1)$ configuration space of four points in $S^3$ is in bijection with an open subset of %with a Kähler structure which is inherited from the one of ${\mathfrak{H}}^{\star }\times {\mathbb{R}}_{>0}$, where ${\mathfrak{H}}^{\star }$ is the affine-rotational group. Since the latter is a Sasakian manifold, the cone ${\mathfrak{H}}^{\star }\times {\mathbb{R}}_{>0}$ is Kähler and thus ${\mathfrak{F}}_4^{\prime \prime }$ inherits this Kähler structure.

21 pages

References in corpus (1)

• The Sasakian Geometry of the Heisenberg Group

Cited by in corpus (1)

• Quasiconformal mappings in the hyperbolic Heisenberg group and a lifting theorem