Displaying similar documents to “Tits geometry, arithmetic groups, and the proof of a conjecture of Siegel.”

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

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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...

On pairs of closed geodesics on hyperbolic surfaces

Nigel J. E. Pitt (1999)

Annales de l'institut Fourier

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In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups Γ . This links the intersection angles and common perpendiculars of pairs of closed geodesics on Γ / H with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian Δ . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.

Differential geometry of grassmannians and the Plücker map

Sasha Anan’in, Carlos Grossi (2012)

Open Mathematics

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Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.

Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar (2014)

Open Mathematics

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For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.