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].