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The notion of a local line bundle on a manifold, classified by 2-cohomology with real
coefficients, is introduced. The twisting of pseudodifferential operators by such a line
bundle leads to an algebroid with elliptic elements with real-valued index, given by a
twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and
Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold
is shown to yield the star products...
Dans cet article nous rappelons la définition d’un star-produit, et étudions et classifions les star-produits sur un fibré cotangent complexe. Ce sujet a fait l’objet d’une conférence en l’honneur de V. Guillemin en septembre 1998 ; il est dévelopé plus en détail dans [2]. Cet article est dédié à la mémoire de M. Flato et A. Lichnerowicz, disparus peu de temps après la conférence, et qui ont grandement contribué au sujet.
In this paper we show that the windings of geodesics around the cusps of a Riemann surface of a finite area, behave asymptotically as independent Cauchy variables.
We produce a stochastic regularization of the Poisson-Sigma model of Cattaneo-Felder, which is an analogue regularization of Klauder’s stochastic regularization of the hamiltonian path integral [23] in field theory. We perform also semi-classical limits.
We give a canonical construction of an “isotropic average” of given -close isotropic submanifolds of a symplectic manifold. For this purpose we use an improvement (obtained in collaboration
with H. Karcher) of Weinstein’s submanifold averaging theorem and apply “Moser’s trick”. We also present an application to Hamiltonian group actions.
In [Ch00], Chekanov showed that the Hofer norm on the Hamiltonian diffeomorphism group of a geometrically bounded symplectic manifold induces a nondegenerate metric on the orbit of any compact Lagrangian submanifold under the group. In this paper we consider the orbits of more general submanifolds. We show that, for the Chekanov–Hofer pseudometric on the orbit of a closed submanifold to be a genuine metric, it is necessary for the submanifold to be coisotropic, and we show that this condition is...
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.
La caustique d?un point sur une variété riemannienne est l?ensemble des points d?intersection des géodésiques infiniment voisins partant de ce point. Jacobi a remarqué, en utilisant un raisonnement topologique, que la caustique d?un point sur une surface convexe fermée doit avoir des points de rebroussement. Il a aussi annoncé (sans démonstration) que le nombre de ces points est quatre pour les caustiques sur les surfaces d?ellipsoïdes (Jacobi, 1964). Dans cette note j?essaie d?inclure les théorèmes...
We give a complete classification of surfaces with parallel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces.
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