Several cohomology algebras connected with Poisson structure.
Shoikhet's conjecture and Duflo isomorphism on (co)invariants.
Singular Lefschetz pencils.
Singular Poisson reduction of cotangent bundles.
We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
Singular Poisson-Kähler geometry of certain adjoint quotients
The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.
Singular reduction of generalized complex manifolds.
Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Singularities of Poisson and Nambu structures
Skein quantization of Poisson algebras of loops on surfaces
-trivial deformations of -modules of symbols.
Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry
We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...
Slant submanifolds with prescribed scalar curvature into cosymplectic space form.
Some lagrangian invariants of symplectic manifolds
The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by (resp. ) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to . That is to say, there is a bilinear map , which is invariant under F-preserving symplectic diffeomorphisms....
Some liftings of Poisson structures to Weil bundles
We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
Some perturbation results for non-linear problems
We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
Some properties of a closed concircular almost contact manifold.
Some properties of tangent Dirac structures of higher order
Let be a smooth manifold. The tangent lift of Dirac structure on was originally studied by T. Courant in [3]. The tangent lift of higher order of Dirac structure on has been studied in [10], where tangent Dirac structure of higher order are described locally. In this paper we give an intrinsic construction of tangent Dirac structure of higher order denoted by and we study some properties of this Dirac structure. In particular, we study the Lie algebroid and the presymplectic foliation...
Some remarks on tubular neighborhoods and gluing in Morse-Floer homology
We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.
Some results for generalized cochains.
Some type of semisymmetry on two classes of almost Kenmotsu manifolds
The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a -almost Kenmotsu manifold satisfying the curvature condition is locally isometric to the hyperbolic space . Also in -almost Kenmotsu manifolds the following conditions: (1) local symmetry , (2) semisymmetry , (3) , (4) , (5) locally isometric to the hyperbolic space are equivalent. Further, it is proved that a -almost Kenmotsu manifold satisfying...