Legendrian foliations on almost -manifolds.
Lemme de Moser feuilleté et clasifications des variétés de Poisson régulières.
Regular Poisson structures with fixed characteristic foliation F are described by means of foliated symplectic forms. Associated to each of these structures, there is a class in the second group of foliated cohomology H2(F). Using a foliated version of Moser's lemma, we study the isotopy classes of these structures in relation with their cohomology class. Explicit examples, with dim F = 2, are described.
Les -variétés symplectiques et leur classification en dimension 4
Levi-Flat submanifolds and holomorphic extension of foliations
Lie Algebra bundles on s-Kähler manifolds, with applications to Abelian varieties
We prove that one can obtain natural bundles of Lie algebras on rank two -Kähler manifolds, whose fibres are isomorphic respectively to , and . These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of Kähler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of on (rational) Hodge classes of Abelian varieties with rational period matrix.
Lie contact manifolds. II.
Lie groups with no left invariant complex structures
Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles
The second order transverse bundle of a foliated manifold carries a natural structure of a smooth manifold over the algebra of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a -smooth foliated diffeomorphism between two second order transverse bundles maps...
Lifts of structures on manifolds.
Linear transformations of -connections in . II.
Liouville forms in a neighborhood of an isotropic embedding
A Liouville form on a symplectic manifold is by definition a potential of the symplectic form . Its center is given by . A normal form for certain Liouville forms in a neighborhood of its center is given.
Locally conformal almost cosymplectic manifolds
Locally conformal cosymplectic manifolds and time-dependent Hamiltonian systems
We show that locally conformal cosymplectic manifolds may be seen as generalized phase spaces of time-dependent Hamiltonian systems. Thus we extend the results of I. Vaisman for the time-dependent case.
Locally conformal symplectic manifolds.
Manifolds admitting stable forms
In this note we give a direct method to classify all stable forms on as well as to determine their automorphism groups. We show that in dimensions 6, 7, 8 stable forms coincide with non-degenerate forms. We present necessary conditions and sufficient conditions for a manifold to admit a stable form. We also discuss rich properties of the geometry of such manifolds.
Maps between almost Kähler manifolds and framed -manifolds.
Maslov indices on the metaplectic group
We use the properties of to construct functions associated with the elements of the lagrangian grassmannian (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between and a subset of , equipped with appropriate algebraic and topological structures.
Mathematical instanton bundles on P2n+1.
Mean curvature vector and symplectic topology of Lagrangian submanifolds in Einstein-Kähler manifolds.
Metric of special 2F-flat Riemannian spaces
In this paper we find the metric in an explicit shape of special -flat Riemannian spaces , i.e. spaces, which are -planar mapped on flat spaces. In this case it is supposed, that is the cubic structure: .