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We characterize an important class of generalized projective geometries $(X, X^{'})$ by the following essentially equivalent properties: (1) $(X, X^{'})$ admits a central null-system; (2) $(X, X^{'})$ admits inner polarities: (3) $(X, X^{'})$ is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...

The group of biholomorphic automorphisms of symmetric Siegel domains and its topology

José-María Isidro, Jean-Pierre Vigué (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Helgason-Fourier transform for symmetric spaces. II.

Mohanty, Parasar, Ray, Swagato K., Sarkar, Rudra P., Sitaram, Alladi (2004)

Journal of Lie Theory

The infinite Brownian loop on a symmetric space.

Jean-Philippe Anker, Philippe Bougerol, Thierry Jeulin (2002)

Revista Matemática Iberoamericana

The Plancherel formula for the pseudo-riemannian space $SL (n, ℝ) / GL (n - 1, ℝ)$

G. Van Dijk, M. Poel (1986)

Compositio Mathematica

The product formula for the spherical functions on symmetric spaces of noncompact type.

Graczyk, Piotr, Sawyer, Patrice (2003)

Journal of Lie Theory

The proportionality constant for the simplicial volume of locally symmetric spaces

Michelle Bucher-Karlsson (2008)

Colloquium Mathematicae

We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.

The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces

Michael Kapovich, John J. Millson (1996)

Compositio Mathematica

The spectra and the symmetric structure on a compact symmetric space.

Tsagas, Grigorios, Kobotis, Apostolos (1996)

Balkan Journal of Geometry and its Applications (BJGA)

The spherical transform for homogeneous vector bundles over Riemannian symmetric spaces.

Camporesi, Roberto (1997)

Journal of Lie Theory

The Stable Topological-hyperbolic Space Form Problem for Complete Manifolds of Finite Volume.

W.C. Hsiang, F.T. Farrell (1982)

Inventiones mathematicae

The tangent bundle of $p^{r}$ -velocities over a homogeneous space

Jacek Gancarzewicz, Modesto R. Salgado (1991)

Czechoslovak Mathematical Journal

The values of sectional curvature in indefinite metrics.

R.S. Kulkarni (1979)

Commentarii mathematici Helvetici

Three-dimensional conformally flat pseudo-symmetric spaces of constant type

Norio Hashimoto, Masami Sekizawa (2000)

Archivum Mathematicum

An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.

Three-dimensional locally symmetric almost Kenmotsu manifolds

Yaning Wang (2016)

Annales Polonici Mathematici

We prove that a three-dimensional almost Kenmotsu manifold is locally symmetric if and only if it is locally isometric to either the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4)×ℝ.

Time-like isothermic surfaces associated to Grassmannian systems.

Dussan, M.P., Magid, M.A. (2005)

Documenta Mathematica

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