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arxiv 1507.06921 v3 pith:D5WFHRXT submitted 2015-07-24 math.DG math.GT

Proper quasi-homogeneous domains in flag manifolds and geometric structures

Andrew Zimmer This is my paper
classification math.DG math.GT
keywords domainsflagmanifoldsexamplesexistmanymetricprojective
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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 $(G,X)$-structures.

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    Defines Kobayashi-type pseudometric on domains in real-type Nagano spaces; proves it is a metric iff domain avoids photon minus point, and is never Gromov hyperbolic in higher rank for strongly R-proper dually convex ...