Remarks on homogeneous manifolds satisfying Levi conditions
Alan Huckleberry
TL;DR
This paper explores the properties of homogeneous complex manifolds under Levi conditions, focusing on convexity, concavity, and classification of flag domains, highlighting their pseudoconvexity and pseudoconcavity characteristics.
Contribution
It provides a detailed classification of pseudoconvex flag domains and discusses the convexity and concavity properties of these manifolds, extending classical results.
Findings
Classification of pseudoconvex flag domains
Flag domains that are generic are pseudoconcave
Discussion of convexity and concavity properties
Abstract
Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in some detail. A precise classification of pseudoconvex flag domains is given. It is shown that flag domains which are in a certain sense generic are pseudoconcave.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Geometry and complex manifolds