Geometry & Topology

Rigidity of convex divisible domains in flag manifolds

Wouter Van Limbeek and Andrew Zimmer

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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 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 ) .

Article information

Source
Geom. Topol., Volume 23, Number 1 (2019), 171-240.

Dates
Received: 16 May 2017
Accepted: 21 July 2018
First available in Project Euclid: 12 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.gt/1552356081

Digital Object Identifier
doi:10.2140/gt.2019.23.171

Mathematical Reviews number (MathSciNet)
MR3921319

Zentralblatt MATH identifier
07034545

Subjects
Primary: 53C24: Rigidity results 57N16: Geometric structures on manifolds [See also 57M50]
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 22F50: Groups as automorphisms of other structures 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 57S30: Discontinuous groups of transformations

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

Citation

Van Limbeek, Wouter; Zimmer, Andrew. Rigidity of convex divisible domains in flag manifolds. Geom. Topol. 23 (2019), no. 1, 171--240. doi:10.2140/gt.2019.23.171. https://projecteuclid.org/euclid.gt/1552356081


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