Related papers: Closed Geodesics in Lorentzian Surfaces

We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to…

Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. Assume $X$ is not homothetic to a metric graph with integer edge lengths. Let $P_t$ be the number of parallel classes of…

We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized…

In this paper, we study three types of helicoidal surfaces in a Lorentzian n--space $\mathbb{E}^n_1$. First, we find the parametrizations of spacelike loxodromes on such spacelike helicoidal surfaces in $\mathbb{E}^n_1$. Then, we make a…

On a surface with a Finsler metric, we investigate the asymptotic growth of the number of closed geodesics of length less than $L$ which minimize length among all geodesic multicurves in the same homology class. An important class of…

We consider exact magnetic flows on closed orientable surfaces. We show that for almost every energy $\kappa$ below Ma\~n\'e's critical value of the universal covering there are always at least three distinct closed magnetic geodesics with…

We prove that any complete (and possibly non-compact) Riemannian manifold $M$ possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in degrees larger than the dimension of $M$, and there are no…

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that…

Let $M$ be a convex cocompact acylindrical hyperbolic 3-manifold of infinite volume, and let $M^*$ denote the interior of the convex core of $M$. In this paper we show that any geodesic plane in $M^*$ is either closed or dense. We also show…

Fix a smooth closed manifold $M$. Let $R_M$ denote the space of all pairs $(g,L)$ such that $g$ is a $C^3$ Riemannian metric on $M$ and the real number $L$ is not the length of any closed $g$-geodesics. A locally constant geodesic count…

In this paper we will show that a Lagrangian, Lorentzian surface $M^2_1$ in a complex pseudo space form $\widetilde M^2_1 (4c)$ is pseudo-isotropic if and only if $M$ is minimal. Next we will obtain a complete classification of all…

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…

On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair of coprime integers $(p,q)$ it was found the numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ and satisfying the…

We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. By an "approximate isometric embedding" we mean an embedding which preserves the energy…

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

We employ min-max methods to construct uncountably many, geometrically distinct, properly embedded geodesic lines in any asymptotically conical surface of non-negative scalar curvature, a setting where minimization schemes are doomed to…

Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.

We show that a compact Lorentzian locally symmetric space is geodesically complete if the Lorentzian factor in the local de Rham-Wu decomposition is of Cahen-Wallach type or if the maximal flat factor is one-dimensional and time-like. Our…

We present a riemannian structure on the disk that has a remarkably rich structure. Geodesics are hypocycloids and the (negative of the) laplacian has integer spectrum with multiplicity the Dirichlet divisor function. Eigenfunctions of the…

We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…