Transitivity of codimension-one Anosov actions of R(k) on closed manifolds

We consider Anosov actions of R(k), k >= 2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of R(k) has dimension one. We prove that if the ambient manifold has dimension greater than k + 2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincare-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

Quantum field theory of (p,0)-forms on kaehler manifolds

In questa tesi abbiamo studiato la quantizzazione di una teoria di gauge di forme differenziali su spazi complessi dotati di una metrica di Kaehler. La particolarità di queste teorie risiede nel fatto che esse presentano invarianze di gauge riducibili, in altre parole non indipendenti tra loro. L'invarianza sotto trasformazioni di gauge rappresenta uno dei pilastri della moderna comprensione del mondo fisico. La caratteristica principale di tali teorie è che non tutte le variabili sono effettivamente presenti nella dinamica e alcune risultano essere ausiliarie. Il motivo per cui si preferisce adottare questo punto di vista è spesso il fatto che tali teorie risultano essere manifestamente covarianti sotto importanti gruppi di simmetria come il gruppo di Lorentz. Uno dei metodi più usati nella quantizzazione delle teorie di campo con simmetrie di gauge, richiede l'introduzione di campi non fisici detti ghosts e di una simmetria globale e fermionica che sostituisce l'iniziale invarianza locale di gauge, la simmetria BRST. Nella presente tesi abbiamo scelto di utilizzare uno dei più moderni formalismi per il trattamento delle teorie di gauge: il formalismo BRST Lagrangiano di Batalin-Vilkovisky. Questo metodo prevede l'introduzione di ghosts per ogni grado di riducibilità delle trasformazioni di gauge e di opportuni “antifields" associati a ogni campo precedentemente introdotto. Questo formalismo ci ha permesso di arrivare direttamente a una completa formulazione in termini di path integral della teoria quantistica delle (p,0)-forme. In particolare esso permette di dedurre correttamente la struttura dei ghost della teoria e la simmetria BRST associata. Per ottenere questa struttura è richiesta necessariamente una procedura di gauge fixing per eliminare completamente l'invarianza sotto trasformazioni di gauge. Tale procedura prevede l'eliminazione degli antifields in favore dei campi originali e dei ghosts e permette di implementare, direttamente nel path integral condizioni di gauge fixing covarianti necessari per definire correttamente i propagatori della teoria. Nell'ultima parte abbiamo presentato un’espansione dell’azione efficace (euclidea) che permette di studiare le divergenze della teoria. In particolare abbiamo calcolato i primi coefficienti di tale espansione (coefficienti di Seeley-DeWitt) tramite la tecnica dell'heat kernel. Questo calcolo ha tenuto conto dell'eventuale accoppiamento a una metrica di background cosi come di un possibile ulteriore accoppiamento alla traccia della connessione associata alla metrica.

Almost Conformal Transformation in a Class of Riemannian Manifolds

We consider a 3-dimensional Riemannian manifold V with a metric g and an a±nor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conformaly related. In this case we get some properties.

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Multi-shot person re-identification via relational stein divergence

Person re-identification is particularly challenging due to significant appearance changes across separate camera views. In order to re-identify people, a representative human signature should effectively handle differences in illumination, pose and camera parameters. While general appearance-based methods are modelled in Euclidean spaces, it has been argued that some applications in image and video analysis are better modelled via non-Euclidean manifold geometry. To this end, recent approaches represent images as covariance matrices, and interpret such matrices as points on Riemannian manifolds. As direct classification on such manifolds can be difficult, in this paper we propose to represent each manifold point as a vector of similarities to class representers, via a recently introduced form of Bregman matrix divergence known as the Stein divergence. This is followed by using a discriminative mapping of similarity vectors for final classification. The use of similarity vectors is in contrast to the traditional approach of embedding manifolds into tangent spaces, which can suffer from representing the manifold structure inaccurately. Comparative evaluations on benchmark ETHZ and iLIDS datasets for the person re-identification task show that the proposed approach obtains better performance than recent techniques such as Histogram Plus Epitome, Partial Least Squares, and Symmetry-Driven Accumulation of Local Features.