Related papers: Closed Geodesics in Lorentzian Surfaces
In this article, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder $M\simeq S^1\times\mathbb{R}$ or a complete Riemannian plane $M\simeq\mathbb{R}^2$ leads to having…
We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly…
We uncover some connections between the topology of a complete Riemannian surface M and the minimum number of vertices, i.e., critical points of geodesic curvature, of closed curves in M. In particular we show that the space forms with…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
Conditions for the existence of closed geodesics is a classic, much-studied subject in Riemannian geometry, with many beautiful results and powerful techniques. However, many of the techniques that work so well in that context are far less…
This article deals with the set of closed geodesics on complete finite type hyperbolic surfaces. For any non-negative integer $k$, we consider the set of closed geodesics that self-intersect at least $k$ times, and investigate those of…
The aim of this work is the study of geodesics on Lorentzian homogeneous spaces of the form $M=G/\Lambda$, where $G$ is a solvable Lie group endowed with a bi-invariant Lorentzian metric and $\Lambda < G$ is a cocompact lattice. Conditions…
We show that on every compact Riemannian 2-orbifold there exist infinitely many closed geodesics of positive length.
We investigate under which assumptions an orientable pseudo-Riemannian geodesic foliations by circles is generated by an $S^1$-action. We construct examples showing that, contrary to the Riemannian case, it is not always true. However, we…
This paper is about a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly…
This note is about a type of quantitative density of closed geodesics on closed hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic that $\varepsilon$-fills the surface.
We show that on any translation surface, if a regular point is contained in a simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in the unit circle. Moreover, the set of…
In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2.
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
In this paper we prove that for every bumpy Finsler metric $F$ on every rationally homological $n$-dimensional sphere $S^n$ with $n\ge 2$, there exist always at least two distinct prime closed geodesics.
We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth…
We prove the Morse relations for the set of all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of every geodesic…
We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations.…
We obtain Margulis-type asymptotic estimates for the number of free homotopy classes of closed geodesics on certain manifolds without conjugate points. Our results cover all compact surfaces of genus at least 2 without conjugate points.