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

Let (M, 0T ) be a compact strongly pseudo convex CR structure with dimRM = 2n − 1. 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 n-form with the condition H1(M,OM) = 0 and H1 M,∧n−1(T )∗ Z1, where Z1 is introduced in [Compositio Math. 85 (1993) 57–85].  2004 Elsevier Inc. All rights reserved.