Related papers: Geodesic completeness of diagonal $G_2$ metrics
We analyse the geodesics' dynamics in cylindrically symmetric vacuum spacetimes with Lambda>0 and compare it to the Lambda=0 and Lambda<0 cases. When Lambda>0 there are two singularities in the metric which brings new qualitative features…
We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, deforming the metric of a compact locally symmetric space of nonconstant negative curvature. Candidates for such example as the product metric…
It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries,…
We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second derivatives. This includes the full $H^2$-metric without zero…
Two general-relativistic hydrodynamical models are considered: a model of self-gravitating static configurations of perfect fluid and a model of steady accretion of fluid onto a black hole. We generalise analytic results obtained for the…
In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
In this article, we assume that a cold charged perfect fluid is constructing a spherical relativistic star. Our purpose is the investigation of the dynamical properties of its exterior geometry, through simulating the geodesic motion of a…
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…
A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold…
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of…
We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is…
In this paper causal geodesic completeness of FLRW cosmological models is analysed in terms of generalised power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual…
We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for…
In this survey article we gather classical as well as recent results on minimal geodesics of Riemannian or Finsler metrics, giving special attention to the two-dimensional case. Moreover, we present open problems together with some first…
We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed…
The $L^2$-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type $M$ in a Riemannian manifold $(N,g)$ induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that…