Geometric interpretation of curvature tensors and pseudotensors of a space with a nonsymmetric affine connection.
Geometric interpretations of some Jordan algebras.
Geometric mean curvature lines on surfaces immersed in
Geometric methods for solving Codazzi and Monge-Ampère equations.
Geometric modular action and transformation groups
Geometric P.D.E.'s with isolated singularities.
Geometric physics.
Geometric properties of a sequence of standard minimal immersions between spheres
Geometric properties of Lie hypersurfaces in a complex hyperbolic space
We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.
Geometric Properties of Minimal Surfaces with Free Boundaries.
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 realization of discrete series for semisimple symmetric spaces.
Geometric realizations of bi-Hamiltonian completely integrable systems.
Geometric renormalization of large energy wave maps
There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy of the...
Geometric structure of tubes and bands of zero mean curvature.
Geometric structures associated with certain dynamical systems. (Structures géométriques associées à certains systèmes dynamiques.)
Geometric Structures in Bundlesof Associative Algebras
The article deals with bundles of linear algebra as a specifications of the case of smooth manifold. It allows to introduce on smooth manifold a metric by a natural way. The transfer of geometric structure arising in the linear spaces of associative algebras to a smooth manifold is also presented.