Remarks on homogeneous manifolds satisfying Levi conditions

Details Remarks on homogeneous manifolds satisfying Levi conditions Remarks on homogeneous manifolds satisfying Levi conditions

2010-03-31

arxiv.org/abs/1003.5971v1

Bollettino U.M.I. (9) {\bf III} (2010) 1-23

Mathematics

Complex Variables

The article is dedicated to the memory of Aldo Andreotti

Scientific paper

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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