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Finitude géométrique en géométrie de Hilbert

Mickaël Crampon, Ludovic marquis (2014)

Annales de l’institut Fourier

On étudie la notion de finitude géométrique pour certaines géométries de Hilbert définies par un ouvert strictement convexe à bord de classe  𝒞 1 .La définition dans le cadre des espaces Gromov-hyperboliques fait intervenir l’action du groupe discret considéré sur le bord de l’espace. On montre, en construisant explicitement un contre-exemple, que cette définition doit être renforcée pour obtenir des définitions équivalentes en termes de la géométrie de l’orbifold quotient, similaires à celles obtenues...

Finsler Conformal Lichnerowicz-Obata conjecture

V. S. Matveev, H.-B. Rademacher, M. Troyanov, A. Zeghib (2009)

Annales de l’institut Fourier

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

Finsler metrics with propierties of the Kobayashi metric on convex domains.

Myung-Yull Pang (1992)

Publicacions Matemàtiques

The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesics locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve Σ which has properties of extremal disks. Under...

Flats in 3-manifolds

Michael Kapovich (2005)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Flats in Spaces with Convex Geodesic Bicombings

Dominic Descombes, Urs Lang (2016)

Analysis and Geometry in Metric Spaces

In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes...

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