Volume 23, issue 1 (2019)

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Rigidity of convex divisible domains in flag manifolds

Wouter Van Limbeek and Andrew Zimmer

Geometry & Topology 23 (2019) 171–240
Abstract

In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of $p$–planes in ${ℝ}^{2p}$ when $p>1$. Moreover, this convex divisible domain is a model of the symmetric space associated to the simple Lie group $SO\left(p,p\right)$.

Keywords
flag manifolds, geometric structures, convex divisible domains, Hilbert metric, rigidity, Grassmannian
Mathematical Subject Classification 2010
Primary: 53C24, 57N16
Secondary: 22E40, 22F50, 52A20, 57S30