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Generalized symmetric spaces and minimal models

Anna Dumańska-Małyszko, Zofia Stępień, Aleksy Tralle (1996)

Annales Polonici Mathematici

We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.

Geodesic graphs on special 7-dimensional g.o. manifolds

Zdeněk Dušek, Oldřich Kowalski (2006)

Archivum Mathematicum

In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds M = [ SO ( 5 ) × SO ( 2 ) ] / U ( 2 ) and M = [ SO ( 4 , 1 ) × SO ( 2 ) ] / U ( 2 ) . They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining metrics...

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M M ( ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ) for locally symmetric spaces. Moreover, M ( ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

Groupes de Ping-Pong et comptage

Xavier Thirion (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Dans cet article, nous étudions les propriétés asymptotiques d’une large classe de sous-groupe discrets du groupe linéaire réel : les groupes de Ping-Pong. Nous décrivons leur action sur l’espace projectif réel et le comportement à l’infini de leur fonction de comptage.

Groupes de Schottky et comptage

Jean-François Quint (2005)

Annales de l’institut Fourier

Soient X un espace symétrique de type non compact et Γ un groupe discret d’isométries de X du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de Γ sur X .

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