Abstract
Let ( M, 0 T″) be a compact strongly pseudo convex CR structure with dim R M=2 n−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 H 1(M, O M)=0 and H 1 M,∧ n−1(T′) ∗ ≃Z 1, where Z 1 is introduced in [Compositio Math. 85 (1993) 57–85].
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