Compact Heisenberg manifolds as CR manifolds
Let \(H_d\) be the (2d+1)-dimensional Heisenberg group, and \(\Gamma\) be a lattice subgroup of it such that the quotient space \(M=\Gamma \setminus H_d\) is compact. Then there is a natural strongly pseudoconvex CR structure on M. Firstly, studying the Fourier analysis on this strongly pseudoconvex CR manifold M, the eigenvalues and eigenforms of the Kohn Laplacian are calculated completely. Secondly, a realization of M as the boundary of a bounded domain in a line bundle over an Abelian variety is obtained, that is: M is in one-to-one correspondence, up to holomorphic/CR equivalence, with the Abelian variety \(C^d / \Lambda\) equipped with a positive line bundle, where \(\Lambda=\pi(\Gamma)\), \(\pi\) is the quotient mapping.
scientific article; zbMATH DE number 2118174
scientific article