Summary: COMPACT CR-SOLVMANIFOLDS AS KšAHLER
BRUCE GILLIGAN AND KARL OELJEKLAUS
Abstract. We give a precise characterization for when a compact CR-
solvmanifold is CR-embeddable in a complex Kšahler manifold. Equiva-
lently this gives a non-Kšahler criterion for complex manifolds containing
CR-solvmanifolds not satisfying these conditions. This paper is the nat-
ural continuation of [OR] and [GOR].
There are many results known about the structure of real solvmanifolds.
One of these is the conjecture of Mostow [Mos], subsequently proved by
L. Auslander, e.g., see [Aus] for the history, that every solvmanifold is a
vector bundle over a compact solvmanifold. In the category of complex
solvmanifolds one would additionally like to understand the structure of
the manifold with respect to complex analytic objects defined on it and,
particularly, the role played by the base of the vector bundle noted above
- this base determines the topology, so does it also control the complex
analysis? Because of the connection with the existence of plurisubharmonic
functions and analytic hypersurfaces, one problem of this type concerns the
existence of a Kšahler metric.