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Displaying 241 – 260 of 790

Formality and the Lefschetz property in symplectic and cosymplectic geometry

Giovanni Bazzoni, Marisa Fernández, Vicente Muñoz (2015)

Complex Manifolds

We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).

Formality theorems: from associators to a global formulation

Gilles Halbout (2006)

Annales mathématiques Blaise Pascal

Let $M$ be a differential manifold. Let $Φ$ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $Φ$ . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on $C^{\infty} (M)$ and its cohomology $(Γ (M, Λ T M), {[-, -]}_{S}$ ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on $G_{\infty}$ -structures, explanation of the...

Formes de contact ayant le même champ de Reeb

Aggoun, Saad (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.In this paper, we study contact forms on a 3-manifold having a common Reeb vector field R. The main result is that when the contact forms induce the same orientation, they are diffeomorphic.

Formule(s) de Pesin

Gilles F. Robert (1989/1990)

Séminaire de théorie spectrale et géométrie

Four dimensional symplectic Lie algebras.

Ovando, Gabriela (2006)

Beiträge zur Algebra und Geometrie

Frame flows on manifolds with pinched negative curvature

M. Brin, H. Karcher (1984)

Compositio Mathematica

Fredholm theory and transversality for the parametrized and for the $S^{1}$ -invariant symplectic action

Frédéric Bourgeois, Alexandru Oancea (2010)

Journal of the European Mathematical Society

We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the $L^{2}$ -gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic $S^{1}$ -invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define $S^{1}$ -equivariant...

$g$ -natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi, Giovanni Calvaruso (2012)

Archivum Mathematicum

We completely classify Riemannian $g$ -natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_{1} M$ of a Riemannian manifold $(M, g)$ . Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$ -natural metric on the unit tangent sphere bundle of a Riemannian surface.

$𝔤$ -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

A Lie version of Turaev’s $\bar{G}$ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$ -quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮, β)$ together with a left $𝔤$ -module structure which acts on $𝔮$ via derivations and for which $β$ is $𝔤$ -invariant. Geometrically, $𝔤$ -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...

GAGA for DQ-algebroids

Hou-Yi Chen (2010)

Rendiconti del Seminario Matematico della Università di Padova

Gauge equivalence of Dirac structures and symplectic groupoids

Henrique Bursztyn, Olga Radko (2003)

Annales de l’institut Fourier

We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants...

Gauge theoretic invariants of Dehn surgeries on knots.

Boden, Hans U., Herald, Christopher M., Kirk, Paul A., Klassen, Eric P. (2001)

Geometry & Topology

General spectral flow formula for fixed maximal domain

Bernhelm Booss-Bavnbek, Chaofeng Zhu (2005)

Open Mathematics

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by...

Generalizations of Melin's inequality to systems

Raymond Brummelhuis (2001)

Journées équations aux dérivées partielles

We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.

Generalized Conley-Zehnder index

Jean Gutt (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit $1$ as an eigenvalue. Robbin and Salamon define a generalization of the Conley-Zehnder index for any continuous path of symplectic matrices; this generalization is half integer valued. It is based on a Maslov-type index that they define for a continuous path of Lagrangians in a symplectic vector space $(W, \bar{Ω})$ , having chosen a given reference...

Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems.

Ershov, Yu.V., Yakovlev, E.I. (2008)

Sibirskij Matematicheskij Zhurnal

Generalized Kählerian manifolds and transformation of generalized contact structures

Habib Bouzir, Gherici Beldjilali, Mohamed Belkhelfa, Aissa Wade (2017)

Archivum Mathematicum

The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.

Generalized Lie bialgebroids and strong Jacobi-Nijenhuis structures.

D. Iglesias-Ponte, J. C. Marrero (2002)

Extracta Mathematicae

Generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds

Amalendu Ghosh (2015)

Annales Polonici Mathematici

We consider generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds. First, we prove that a complete Sasakian manifold M admitting a generalized m-quasi-Einstein metric is compact and isometric to the unit sphere $S^{2 n + 1}$ . Next, we generalize this to complete K-contact manifolds with m ≠ 1.

Generalized PN manifolds and separation of variables

Fernand Pelletier, Patrick Cabau (2008)

Banach Center Publications

The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.

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