Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0979.52001
Verovic, Patrick
A rigidity result for Hilbert metrics. (Un résultat de rigidité pour les métriques de Hilbert.) (French)
[A] Séminaire de théorie spectrale et géométrie. Année 1999-2000. St. Martin d'Hères: Université de Grenoble I, Institut Fourier, Sémin. Théor. Spectr. Géom. 18, 171-173 (2000).

The author proves the following result: Let $ \Cal{C} $ be an open, convex and bounded set of $ \Bbb{R} ^n $ such that its boundary $ \partial \Cal{C} $ is a strictly convex hypersurface of $ \Bbb{R} ^n $ of class $ C ^3 $. If $ \partial \Cal{C} $ is not an ellipsoid then each subgroup of $ \text{Iso} (\Cal{C}, d _{\Cal{C}}) $, where $ d _{\Cal{C}} $ is the Hilbert metric, which does not act proper and discontinuous on $ \Cal{C} $ is a finite one.
[Mircea Puta (Timişoara)]

MSC 2000:: *52A20 Convex sets in n dimensions
53C22 Geodesics

Keywords: Hilbert metric; rigidity; discontinuous

Cited in: Zbl 1007.53055

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]