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.
Geometrische Krystallographie [Book]
Geometry of the Kepler system in coherent states approach
Geometry on the group of Hamiltonian diffeomorphisms.
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.
Global finite generating functions for field theory
We introduce an infinite-dimensional version of the Amann-Conley-Zehnder reduction for a class of boundary problems related to nonlinear perturbed elliptic operators with symmetric derivative. We construct global generating functions with finite auxiliary parameters, describing the solutions as critical points in a finite-dimensional space.
Gluing complex discs to Lagrangian manifolds by Gromov’s method
The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.
Graded lagrangian submanifolds
Gradient-Like and Integrable Vector Fields on IR2.