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A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek (2004)

Open Mathematics

The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].

A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

Eugene Karolinsky (2000)

Banach Center Publications

Let G be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous G-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous G-spaces and Lagrangian subalgebras in the double D𝖌 (here 𝖌 = Lie G). A geometric interpretation of some Poisson homogeneous G-spaces is also proposed.

A generalized exponential map for an affinely homogeneous cone

Umberto Sampieri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Dato un cono V aperto non vuoto, convesso, regolare e affinemente omogeneo in uno spazio vettoriale reale W di dimensione finita si prova che per ogni v appartenente a V esiste un diffeomorfismo E v : W V che soddisfa le condizioni seguenti E1) E v ( 0 ) = v ; E2) det ( d E v ( y ) ) = Φ V ( E v ( y ) ) - 1 per ogni y appartenente a W ove Φ V : V 𝐑 + è la funzione caratteristica di V .

A geometry on the space of probabilities (II). Projective spaces and exponential families.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...

A property of Wallach's flag manifolds

Teresa Arias-Marco (2007)

Archivum Mathematicum

In this note we study the Ledger conditions on the families of flag manifold ( M 6 = S U ( 3 ) / S U ( 1 ) × S U ( 1 ) × S U ( 1 ) , g ( c 1 , c 2 , c 3 ) ) , ( M 12 = S p ( 3 ) / S U ( 2 ) × S U ( 2 ) × S U ( 2 ) , g ( c 1 , c 2 , c 3 ) ) , constructed by N. R. Wallach in (Wallach, N. R., Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), 276–293.). In both cases, we conclude that every member of the both families of Riemannian flag manifolds is a D’Atri space if and only if it is naturally reductive. Therefore, we finish the study of M 6 made by D’Atri and Nickerson in (D’Atri, J. E., Nickerson, H. K., Geodesic...

Affine reductive spaces

OLDRICH KOWALSKI (1979)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Amenable hyperbolic groups

Pierre-Emmanuel Caprace, Yves de Cornulier, Nicolas Monod, Romain Tessera (2015)

Journal of the European Mathematical Society

We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...

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