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Proper quasi-homogeneous domains in flag manifolds and geometric structures
In this paper we study domains in flag manifolds which are bounded in an
affine chart and whose projective automorphism group acts co-compactly. In
contrast to the many examples in real projective space, we will show that no
examples exist in many flag manifolds. Moreover, in the cases where such
domains can exist, we show that they satisfy a natural convexity condition and
have an invariant metric which generalizes the Hilbert metric. As an
application we give some restrictions on the developing map for certain
-structures.Comment: 21 pages, v3: minor corrections. Final version to appear in Annales
de l'Institut Fourie
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