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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 $ℱ$ , la complétude du flot se lit sur l’holonomie de $ℱ$ . On montre ainsi qu’il n’existe pas de flots nul-géodésiques lisses sur $S^{3}$ . On montre aussi qu’un $2$ -tore lorentzien est nul-complet si et seulement si ses feuilletages de type lumière...

Complex geometry of generalized annuli.

de Fabritiis, Ch. (2003)

Advances in Geometry

Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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

Karsten Grove, Stephen Halperin (1982)

Publications Mathématiques de l'IHÉS

Convergence of Bergman geodesics on ${CP}^{1}$

Jian Song, Steve Zelditch (2007)

Annales de l’institut Fourier

The space $ℋ$ of Kähler metrics in a fixed Kähler class on a projective Kähler manifold $X$ is an infinite dimensional symmetric space whose geodesics $ω_{t}$ are solutions of a homogeneous complex Monge-Ampère equation in $A \times X$ , where $A \subset ℂ$ is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials $ϕ (t, z)$ of $ω_{t}$ may be approximated in a weak $C^{0}$ sense by geodesics $ϕ_{N} (t, z)$ of the finite dimensional symmetric space of Bergman metrics of height $N$ . In this article we prove that $ϕ_{N} (t, z) \to ϕ (t, z)$ in $C^{2} ([0, 1] \times X)$ in the case of...

Convex Surfaces Whose Geodesics Are Planar.

G.R. Burton (1977)

Monatshefte für Mathematik

Cordes et géodésiques fermées

Claire M. C. Baribaud (1996/1997)

Séminaire de théorie spectrale et géométrie

Correspondances géodésiques entre les surfaces euclidiennes à singularités coniques.

Mohammed Mostefa Mesmoudi (1996)

Revista Matemática Iberoamericana

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

David D. Bleecker (1981)

Colloquium Mathematicae

Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature.

Katsuhiro Shiohama (1985)

Commentarii mathematici Helvetici

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