Canonical coordinates for coadjoint orbits of completely solvable groups.
Canonical equivariant extensions using classical Hodge theory.
Canonical forms for -structures in pseudo-riemannian manifolds
Canonical Poisson-Nijenhuis structures on higher order tangent bundles
Let M be a smooth manifold of dimension m>0, and denote by the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and the complete lift of Π on TM. In a previous paper, we have shown that is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002), 243-257],...
Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.
We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σrk=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.
Cartan connections and momentum maps
Certain contact metrics satisfying the Miao-Tam critical condition
We study certain contact metrics satisfying the Miao-Tam critical condition. First, we prove that a complete K-contact metric satisfying the Miao-Tam critical condition is isometric to the unit sphere . Next, we study (κ,μ)-contact metrics satisfying the Miao-Tam critical condition.
Characteristic vector fields of generic distributions of corank 2
Characterization of diffeomorphisms that are symplectomorphisms
Let and be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that .
Chern classes of integral submanifolds of some contact manifolds.
Chirurgies de Dehn admissibles dans les variétés de contact tendues
On décrit un exemple de variété de contact universellement tendue qui devient vrillée après une chirurgie de Dehn admissible sur un entrelacs transverse.
Classification analytique de structures de Poisson
Notre étude porte sur une catégorie de structures de Poisson singulières holomorphes au voisinage de et admettant une forme normale formelle polynomiale i.e. un nombre fini d’invariants formels. Les séries normalisantes sont divergentes en général. On montre l’existence de transformations normalisantes holomorphes sur des domaines sectoriels de la forme , où est un monôme associé au problème. Il suit une classification analytique.
Classification géométrique des structures internes des systèmes dynamiques à deux spins
Classification of locally symmetric contact metric manifolds.
Classification of -Ricci-semisymmetric -manifolds.
Classifications of star products and deformations of Poisson brackets
On the algebra of functions on a symplectic manifold we consider the pointwise product and the Poisson bracket; after a brief review of the classifications of the deformations of these structures, we give explicit formulas relating a star product to its classifying formal Poisson bivector.
Closed forms on symplectic fibre bundles.
Closed geodesics, periods and arithmetic of modular forms.
Closed Legendre geodesics in Sasaki manifolds.
Cluster ensembles, quantization and the dilogarithm
A cluster ensemble is a pair of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group . The space is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism . The space is equipped with a closed -form, possibly degenerate, and the space has a Poisson structure. The map is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role...