Homogeneous almost complex manifolds and their compact quotients

Abstract

This paper investigates the (non)existence of compact quotients of the homogeneous almost-complex strongly-pseudoconvex manifolds discovered and classified by Gaussier–Sukhov [Wong–Rosay theorem in almost complex manifolds, http:www.arXiv.org:math.CV/0307335 ; On the geometry of model almost complex manifolds with boundary, Math. Z. 254(3) (2006) 567–589] and Lee [Domains in almost complex manifolds with an automorphism orbit accumulating at a strongly pseudoconvex boundary point, Michigan Math. J. 54(1) (2006) 179–205; Strongly pseudoconvex homogeneous domains in almost complex manifolds, J. Reine Angew. Math. 623 (2008) 123–160].