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

[摘要] Let (M, T-0) be a compact strongly pseudo convex CR structure with dim(R) M = 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 H-1 (M, O-M) = 0 and H-1 (M, boolean AND(n-1)(T')*) similar or equal to Z(1), where Z(1) is introduced in [Compositio Math. 85 (1993) 57-85]. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-01