Lagrange geometry on tangent manifolds.
Lagrange geometry via complex Lagrange geometry.
Lagrange spaces with indicatrices as constant mean curvature surfaces or minimal surfaces.
Lagrange spaces with -metric.
Lagrangian fibrations on hyperkähler manifolds – On a question of Beauville
Let be a compact hyperkähler manifold containing a complex torus as a Lagrangian subvariety. Beauville posed the question whether admits a Lagrangian fibration with fibre . We show that this is indeed the case if is not projective. If is projective we find an almost holomorphic Lagrangian fibration with fibre under additional assumptions on the pair , which can be formulated in topological or deformation-theoretic terms. Moreover, we show that for any such almost holomorphic Lagrangian...
Lagrangian holonomy ; characteristic elements of a lagrangian foliation
Let be a lagrangian foliation on a symplectic manifold . The characteristic elements of such a foliation associated to a lagrangian total transversal are obtained; they are a generalisation of the characteristic elements given by J.J. Duistermaat [5]. This technique is applied to give a classification of the germs of lagrangian foliation along a compact leaf. Several examples of classification are given.
Lagrangian Intersections in Contact Geometry.
Lagrangian submanifolds of quaternion Kaehlerian manifolds satisfying Chen's equality.
Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections
We classify all F2Mm1, m2, n1, n2-natural operators Atransforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle Lfib-fib(Y) on Y. Moreover, we classify all F2Mm1, m2, n1, n2-natural operators B transforming projectable-projectable torsion-free classical linear connections ∇ on fiberedfibered manifolds Y of dimension (m1, m2, n1, n2) into Euler...
Lagrangians and higher order tangent spaces.
L'aire systolique conforme des groupes cristallographiques du plan
Nous établissons des inégalités isosystoliques optimales pour les 17 orbifolds plates en dimension 2 (analogues à l’inégalité classique de Loewner pour le tore), ainsi que pour les quotients du plan hyperbolique par les groupes du triangle.
Laminations et hypersurfaces géodésiques des variétés hyperboliques
Laplacien et géodésiques fermées sur les formes d'espace hyperbolique compactes
Large group actions on manifolds.
Large scale Sobolev inequalities on metric measure spaces and applications.
Large-scale isoperimetry on locally compact groups and applications
We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first...
Le complexe de Koszul en algèbre et topologie
The Koszul complex, as introduced in 1950, was a differential graded algebra which modelled a principal fibre bundle. Since then it has been an effective tool, both in algebra and in topology, for the calculation of homological and homotopical invariants. After a partial summary of these results we recall more recent generalizations of this complex, and some applications.
Le flot géodésique des variétés riemanniennes à courbure négative
Le front d'onde en géométrie sous-riemannienne : le cas Martinet
Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques)