Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein.
Les variétés hyperboliques sont des minima locaux de l'entropie topologique.
Les variétés riemanniennes de dimension quatre pincées
Nous montrons qu’une variété riemannienne de dimension 4 orientable dont la courbure sectionnelle est 4/19-pincée est homéomorphe à la sphère ou au projectif . La preuve utilise une inégalité entre les nombres caractéristiques qui découle d’estimées sur le tenseur de courbure.
L'espace des feuilletages d'un espace analytique compact
Nous construisons sur l’ensemble des feuilletages (avec singulariés) d’un espace analytique compact normal une structure analytique complexe. Dans le cas faiblement kählérien, nous montrons qu’à un point frontière de la compactification naturelle de l’espace des feuilletages est encore associé un feuilletage.
Level sets of Gauss curvature in surfaces of constant mean curvature
Levi-Curvature of Manifolds with a Stein Rational Fibration.
Levi-flat filling of real two-spheres in symplectic manifolds (I)
Let be a manifold with an almost complex structure tamed by a symplectic form . We suppose that has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of can be foliated by the boundaries of pseudoholomorphic discs.
Levi-flat filling of real two-spheres in symplectic manifolds (II)
We consider a compact almost complex manifold with smooth Levi convex boundary and a symplectic tame form . Suppose that is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into . We prove a result on filling by holomorphic discs.
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 algebras of vector fields and generalized foliations.
The main result is a Pursell-Shanks type theorem describing isomorphism of the Lie algebras of vector fields preserving generalized foliations. The result includes as well smooth as real-analytic and holomorphic cases.
Lie contact manifolds. II.
Lie derivatives and natural operators
Lie derivatives on real hypersurfaces in a complex projective space
Lie groups with no left invariant complex structures
Lie theory and the Chern–Weil homomorphism
Lift spaces and generalized connections
Liftings of functions and vector fields to natural bundles [Book]
Lifts and isomorphisms of commutation in bundles of jets.
Lifts of 1-forms to the tangent bundle of higher order