The canonical Kaehler potential on the parameter space of the versal family of CR structures

Let <f>(M,0T″)</f> be a compact strongly pseudo convex CR structure with <f>dimRM=2n-1</f>. Then, in [Michigan Math. J. 50 (2002) 517–549], the construction of the versal family of CR structures is settled. The purpose of this paper is to introduce a canonical Kaehler metric for the parameter space of this versal family if the CR structure admits a normal vector field and a non-vanishing CR <f>n</f>-form with the condition <f>H1(M,OM)=0</f> and where <f>Z1</f> is introduced in [Compositio Math. 85 (1993) 57–85]. [Copyright &y& Elsevier]