Closed Curves and Geodesics with Two Self-Intersections on the Punctured Torus.
Closed geodesics and flat tori in spectral theory on symmetric spaces
Closed geodesics in simply connected Riemannian spaces of negative curvature.
Closed Geodesics on Complete Surfaces.
Closed geodesics on surfaces of genus 0
Collars in PSL.
Compact Riemannian manifolds with homogeneous geodesics.
Comparision of the length of infinite geodesics in manifolds with nonpositive curvature.
Complétude des deux-tores lorentziens
Complétude et flots nul-géodésibles en géométrie lorentzienne
On étudie la complétude géodésique des flots nul-prégéodésiques sur les variétés lorentziennes compactes, ce qui donne une obstruction à être nul-géodésique. On montre que lorsque l’orthogonal du champ de vecteurs engendrant le flot considéré s’intègre en un feuilletage , la complétude du flot se lit sur l’holonomie de . On montre ainsi qu’il n’existe pas de flots nul-géodésiques lisses sur . On montre aussi qu’un -tore lorentzien est nul-complet si et seulement si ses feuilletages de type lumière...
Complex geometry of generalized annuli.
Conjugate-cut loci and injectivity domains on two-spheres of revolution
In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is g = dϕ2 + m(ϕ)dθ2 to the period mapping of the ϕ-variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine...
Contributions of rational homotopy theory to global problems in geometry
Convergence of Bergman geodesics on
The space of Kähler metrics in a fixed Kähler class on a projective Kähler manifold is an infinite dimensional symmetric space whose geodesics are solutions of a homogeneous complex Monge-Ampère equation in , where is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials of may be approximated in a weak sense by geodesics of the finite dimensional symmetric space of Bergman metrics of height . In this article we prove that in in the case of...
Convex Surfaces Whose Geodesics Are Planar.
Cordes et géodésiques fermées
Correspondances géodésiques entre les surfaces euclidiennes à singularités coniques.
A. J. Montesinos has shown that a geodesic correspondence between two complete Riemannian manifolds with transitive topological geodesic flow is a homothety. In this paper we prove a similar result for a conformal geodesic correspondence between two singular flat surfaces with conical singularities and negative concentrated curvature.
Cut loci of closed surfaces without conjugate points
Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature.