DSpace Collection: http://www.openstarts.units.it:80/dspace/handle/10077/4315 2013-06-18T23:39:10Z 2013-06-18T23:39:10Z Irreducible unitary representations of a diffeomorphisms group of an infinite-dimensional real manifold Lüdkovsky, S.V. http://www.openstarts.units.it:80/dspace/handle/10077/4362 2012-11-23T10:53:26Z 1999-01-01T00:00:00Z Title: Irreducible unitary representations of a diffeomorphisms group of an infinite-dimensional real manifold Authors: Lüdkovsky, S.V. Abstract: Groups of diffeomorphisms $Diff_{\beta,\Upsilon}^{t}$ (M) of infinite-dimensionai real Banach manifolds M are defined. Their structure is studied. Irreducible unitary representations of a group of diffeomorphisms associated with quasi-invariant measures on a Banach manifold are constructed. Type: Articolo 1999-01-01T00:00:00Z Determination of convex bodies from $\pm \infty$-chord functions Soranzo, Alessandro http://www.openstarts.units.it:80/dspace/handle/10077/4361 2012-11-23T10:50:05Z 1999-01-01T00:00:00Z Title: Determination of convex bodies from $\pm \infty$-chord functions Authors: Soranzo, Alessandro Abstract: We generalize the concept of i-chord function to the cases $i=+\infty$ and $i=-\infty$, and we extend two results concerning the determination of convex bodies from i-chord functions to those new values of i. Type: Articolo 1999-01-01T00:00:00Z Twistor Bundles of Almost Symplectic Manifolds Nannicini, Antonella http://www.openstarts.units.it:80/dspace/handle/10077/4360 2012-11-23T11:23:43Z 1999-01-01T00:00:00Z Title: Twistor Bundles of Almost Symplectic Manifolds Authors: Nannicini, Antonella Abstract: In this paper we introduce the twistor bundle of a 2n-dimensional almost symplectic manifold M as the quotient bundle $\frac{P\left(M,Sp\left(2n\right)\right)}{U\left(n\right)}$. Given a symplectic connection on M we introduce a natural almost Hermitian structure on the twistor bundle and we prove that this structure is K$\ddot{\textrm{a}}$hler if and only if M is symplectic and the chosen connection has vanishing curvature and (0,2)-part of the torsion. Moreover we prove that in the case of $\mathbb{R}^{2n}$ with standard symplectic structure the twistor bundle turns out to be K$\ddot{\textrm{a}}$hler with constant scalar curvature for a certain class of symplectic connections. Type: Articolo 1999-01-01T00:00:00Z Totally geodesic horizontally conformal maps Mustafa, M.T. http://www.openstarts.units.it:80/dspace/handle/10077/4359 2012-11-23T11:17:25Z 1999-01-01T00:00:00Z Title: Totally geodesic horizontally conformal maps Authors: Mustafa, M.T. Abstract: We obtain a characterization of totally geodesic horizontally conformal maps by a method which arises as a consequence of the Bochner technique for harmonic morphisms. As a geometric consequence we show that the existence of a non-constant harmonic morphism $\textrm{Ø}$ from a compact Riemannian manifold M$^{m}$ of non-negative Ricci curvature to a compact Riemannian manifold of non-positive scalar curvature, forces M$^{m}$ either to be a global Riemannian product of integral manifolds of vertical and horizontal distributions or to be covered by a global Riemannian product. Type: Articolo 1999-01-01T00:00:00Z