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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 2p 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