Rigidity of convex divisible domains in flag manifolds

Van Limbeek, Wouter; Zimmer, Andrew

doi:10.2140/gt.2019.23.171

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Rigidity of convex divisible domains in flag manifolds

Wouter Van Limbeek and Andrew Zimmer

Geometry & Topology 23 (2019) 171–240

DOI: 10.2140/gt.2019.23.171

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 $ℝ^{2 p}$ when $p > 1$ . Moreover, this convex divisible domain is a model of the symmetric space associated to the simple Lie group $SO (p, p)$ .

Keywords

flag manifolds, geometric structures, convex divisible domains, Hilbert metric, rigidity, Grassmannian

Mathematical Subject Classification 2010

Primary: 53C24, 57N16

Secondary: 22E40, 22F50, 52A20, 57S30

References

Publication

Received: 16 May 2017

Accepted: 21 July 2018

Published: 5 March 2019

Proposed: Anna Wienhard

Seconded: Bruce Kleiner, Benson Farb

Authors

Wouter Van Limbeek
Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States

Andrew Zimmer
Department of Mathematics Louisiana State University Baton Rouge, LA United States

Volume 23, issue 1 (2019)