Generalized polarized manifolds.
Generating function polynomials for Legendrian links.
Generic properties of closed geodesics on smooth hypersurfaces.
Generic Properties of Geodesic Flows.
Geodätischer Fluß auf Mannigfaltigkeiten vom hyperbolischen Typ.
Geodesic conjugation of two-step nilmanifolds. (Conjugaison géodésique des nilvariétés de rang deux.)
Geodesic flow and two (super) component analog of the Camassa-Holm equation.
Geodesic Flow on SO(4) and Abelian Surfaces.
Geodesic flows on the Bott-Virasoro group with Dubinskii norm.
Geodesics and Totally Convex Sets on Surfaces.
Geodesics in the compactly supported Hamiltonian diffeomorphism group.
Geodesics on open surfaces containing horns
Geodesics on quadrics and a mechanical problem of C. Neumann.
Geography of symplectic 4-manifolds with Kodaira dimension one.
Geometric Quantization and Multiplicities of Group Representations.
Geometric quantization and no-go theorems
A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a...
Geometric quantization of integrable systems with hyperbolic singularities
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.
Geometric Quantization on Presymplectic Manifolds.
Geometric structures on spaces of weighted submanifolds.
Geometric structures on the tangent bundle of the Einstein spacetime
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.