Homogeneous CR-solvmanifolds as Kahler obstructions
Bruce Gilligan, Karl Oeljeklaus
TL;DR
This paper characterizes when compact homogeneous CR-solvmanifolds can be embedded into Kähler manifolds, providing criteria to identify non-Kähler complex manifolds containing such CR-solvmanifolds.
Contribution
It offers a precise characterization of CR-embeddability of homogeneous CR-solvmanifolds into Kähler manifolds, extending previous work.
Findings
Provides a criterion for CR-embeddability into Kähler manifolds.
Identifies non-Kähler manifolds containing CR-solvmanifolds that do not meet the criteria.
Extends the understanding of the relationship between CR-structures and Kähler geometry.
Abstract
We give a precise characterization when a compact homogeneous CR-solvmanifold is CR-embeddable in a Kahler manifold. Equivalently this gives a non-Kahler criterion for complex manifolds containing CR-solvmanifolds not satisfying these conditions. This paper is the natural continuation of [OR] and [GOR].
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Advanced Algebra and Geometry