Abstract :
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.
