On the geodesics flow of tori without conjugate points.
On the geometric prequantization of brackets.
En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.
On the geometry of the standard -symplectic and Poisson manifolds.
On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
On the integrability of orthogonal distributions in Poisson manifolds.
On the Lengths of Closed Geodesics on Almost Round Spheres.
On the linearization theorem for proper Lie groupoids
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
On the normality of an almost contact -structure on -submanifolds
We study -dimensional -submanifolds of -dimension immersed in a quaternionic space form , , and, in particular, determine such submanifolds with the induced normal almost contact -structure.
On the pullback equation
On the quasi-conformal curvature tensor of a Kenmotsu manifold.
On the Riemann-Lie algebras and Riemann-Poisson Lie groups.
On the topology of Lagrangian submanifolds examples and counter-examples.
On the variety of lagrangian subalgebras, I
On the variety of lagrangian subalgebras, II
On topologically distinct infinite families of exact Lagrangian fillings
In this note we construct examples of closed connected Legendrian submanifolds in high dimensional contact vector space that admit an arbitrary finite number of topologically distinct infinite families of diffeomorphic, but not Hamiltonian isotopic exact Lagrangian fillings.
On variants of Arnold conjecture
In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.
On weakly -symmetric Kenmotsu Manifolds
The object of the present paper is to study weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds. It is shown that weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds are -Einstein.
On -conformally flat contact metric manifolds.
One-dimensional infinitesimal-birational duality through differential operators
The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.
Open books on contact five-manifolds
By using open book techniques we give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. The theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures.