Conditions under which a Geodesic Flow is Anosov.
Conformal Ricci Soliton in Lorentzian -Sasakian Manifolds
In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton is -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian -Sasakian...
Conformally Anosov flows in contact metric geometry.
Conformally equivariant quantization : existence and uniqueness
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-riemannian manifold . In other words, we establish a canonical isomorphism between the spaces of polynomials on and of differential operators on tensor densities over , both viewed as modules over the Lie algebra where . This quantization exists for generic values of the weights of the tensor densities and we compute the critical values of the weights yielding...
Conjugation spaces.
Connecting orbits of time dependent Lagrangian systems
We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.
Connections in regular Poisson manifolds over ℝ-Lie foliations
The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally,...
Connections induced by -tensor fields on cotangent bundles
On cotangent bundles the Liouville field, the Liouville 1-form and the canonical symplectic structure d exist. In this paper interactions between these objects and -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.
Construction de sous-variétés symplectiques
Contact 3-manifolds twenty years since J. Martinet's work
The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on . Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on .
Contact geometry and complex surfaces.
Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions
We study the geometry of multidimensional scalar order PDEs (i.e. PDEs with independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle over a -dimensional contact manifold . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general Monge-Ampère equations (MAEs), we focus our attention to MAEs of...
Contact hamiltonians distinguishing locally certain Goursat systems
For the first time in dimension 9, the Goursat distributions are not locally smoothly classified by their small growth vector at a point. As shown in [M1], in dimension 9 of the underlying manifold 93 different local behaviours are possible and four irregular pairs of them have coinciding small growth vectors. In the present paper we distinguish geometrically objects in three of those pairs. Smooth functions in three variables - contact hamiltonians in the terminology of Arnold, [A] - help to do...
Contact homology and one parameter families of Legendrian knots.
Contact Homology, Capacity and Non-Squeezing in via Generating Functions
Starting from the work of Bhupal we extend to the contact case the Viterbo capacity and Traynor’s construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.
Contact homology of toroidal manifolds. (Homologie de contact des variétés toroïdales.)
Contact Quantization: Quantum Mechanics = Parallel transport
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum systems in terms...
Contractions of to the Heisenberg group and Berezin calculus. (Contraction de vers le groupe de Heisenberg et calcul de Berezin.)
Controlled constructions of Reeb fields and applications. (Constructions contrôlées de champs de Reeb et applications.)
Convexité rationnelle des sous-variétés immergées lagrangiennes