Calabi quasi-morphisms for some non-monotone symplectic manifolds.
Calculation of Rozansky-Witten invariants on the Hilbert schemes of points on a K3 surface and the generalised kummer varieties.
Calculus on Lie algebroids, Lie groupoids and Poisson manifolds [Book]
Calculus on symplectic manifolds
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex. In particular, on complex projective space with its Fubini–Study form and connection, we can build a series of differential complexes akin to the Bernstein–Gelfand–Gelfand complexes from parabolic differential geometry.
Canonical contact forms on spherical CR manifolds
We construct the CR invariant canonical contact form on scalar positive spherical CR manifold , which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold , where is a convex cocompact subgroup of and is the discontinuity domain of . This contact form can be used to prove that is scalar positive (respectively, scalar negative, or scalar vanishing) if and...
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.