Le problème de Yamabe sur des sous domaines de
Le second nombre de Betti d’une variété riemannienne -pincée de dimension 4
On démontre que le second nombre de Betti réel d’une variété riemannienne compacte de dimension 4 à courbure sectionnelle -pincée est majoré par un.
Le spectre des longueurs des surfaces hyperboliques : un exemple de rigidité.
Après avoir présenté quelques résultats récents portant sur l’étude du spectre des longueurs des surfaces hyperboliques avec ou sans singularités, on démontre que les sphères possédant trois points coniques sont, dans leur classe, spectralement rigides.
Le spectre du laplacien agissant sur les formes différentielles
Le spectre du laplacien agissant sur les -formes différentielles d’un fibré en cercle
Le spectre marqué des longueurs des surfaces à courbure négative
Le théorème de Gromoll-Meyer sur les géodésiques fermées
Le volume conforme et ses applications d'après Li et Yau
Leafwise, transversal and mixed 2-jets of bundles over foliated manifolds.
Least Area Incompressible Surfaces in 3-Manifolds.
Least area Tori and 3-manifolds of nonnegative scalar curvature.
Least-volume representatives of homology classes in
Leaves of foliations with a transverse geometric structure of finite type.
In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.
Lectures on generalized complex geometry and supersymmetry
These are the lecture notes from the 26th Winter School “Geometry and Physics", Czech Republic, Srní, January 14 – 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and generalized...
Lefschetz coincidence numbers of solvmanifolds with Mostow conditions
For any two continuous maps , between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of , . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.
Lefschetz fibrations and the Hodge bundle.
Lefschetz fibrations, complex structures and Seifert fibrations on .
Lefschetz fibrations in symplectic geometry.
Left-invariant almost complex structures and the associated metrics on four-dimensional direct products of Lie groups.
Legendrian dual surfaces in hyperbolic 3-space
We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the dualities...