Rigidity of convex divisible domains in flag manifolds

Van Limbeek, Wouter¹ ; Zimmer, Andrew²

¹ Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, United States
² Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States

Geometry & topology, Tome 23 (2019) no. 1, pp. 171-240.

Résumé

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 $SO\left(p,p\right)$.

Détail

DOI : 10.2140/gt.2019.23.171

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

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