Metric rigidity of crystallographic groups.
Metric semi-symmetric -linear connections in the bundle of accelerations.
Metric tensor estimates, geometric convergence, and inverse boundary problems.
Metric tensors for homogeneous, isotropic, 5-dimensional pseudo Riemannian models.
Metric with ergodic geodesic flow is completely determined by unparameterized geodesics.
Metrics and tangent cones of uniformly regular Carnot-Carathéodory spaces.
Metrics in the sphere of a C*-module
Given a unital C*-algebra and a right C*-module over , we consider the problem of finding short smooth curves in the sphere = x ∈ : 〈x, x〉 = 1. Curves in are measured considering the Finsler metric which consists of the norm of at each tangent space of . The initial value problem is solved, for the case when is a von Neumann algebra and is selfdual: for any element x 0 ∈ and any tangent vector ν at x 0, there exists a curve γ(t) = e tZ(x 0), Z ∈ , Z* = −Z and ∥Z∥ ≤ π, such...
Metrics of constant curvature on a Riemann surface with two corners on the boundary
Metrics of Positive Ricci Curvature with Large Diameter.
Metrics of Positive Scalar Curvature on Spheres and the Gromov-Lawson Conjecture.
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.
Metrics with Harmonic Spinors.
Metrics with homogeneous geodesics on flag manifolds
A geodesic of a homogeneous Riemannian manifold is called homogeneous if it is an orbit of an one-parameter subgroup of . In the case when is a naturally reductive space, that is the -invariant metric is defined by some non degenerate biinvariant symmetric bilinear form , all geodesics of are homogeneous. We consider the case when is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group , and we give a simple necessary condition that admits a non-naturally reductive...
Metrics with only finitely many isometry invariant geodesics.
Métriques de Quillen et plongements complexes
Métriques d'Einstein à cusps et équations de Seiberg-Witten.
Métriques d'Einstein-Kähler sur les variétés de Fano : obstructions et existence
Métriques kählériennes à courbure scalaire constante : unicité, stabilité
Un des problèmes les plus intéressants de la géométrie différentielle complexe consiste à comprendre les classes de Kähler de variétés complexes admettant des métriques à courbure scalaire constante. La question de l’unicité a été récemment résolue par Donaldson, Mabuchi, Chen–Tian. Des liens forts avec la stabilité algébrique des variétés ont été mis en évidence. L’exposé s’attachera à exposer les idées nouvelles qui ont mené à ces résultats.
Métriques kählériennes et fibrés holomorphes
Métriques riemanniennes holomorphes en petite dimension
Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension . Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension .