Related papers: Open problems and questions about geodesics

In this paper, we study and almost completely classify contact structures on closed 3--manifolds which are totally geodesic for some Riemannian metric. Due to previously known results, this amounts to classifying contact structures on…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

In this paper we solve the fractional anisotropic Calder\'on problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian,…

The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties…

The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…

On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered. By means of this normalization, one can construct the…

The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understood in the case of surfaces. For surfaces of revolution…

We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups and apply…

In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator $\Delta_g+q$ on a Riemannian surface can determine its topological, differential, and metric structure. Earlier work of this type assumes a…

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The…

We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…

We study geodesics on a planar Riemann surface of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these…

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. The main result is the classification of compact simply…

In this paper we develop an intrinsic formalism to study the topology, smooth structure, and Riemannian geometry of the Wasserstein space of a closed Riemannian manifold. Our formalism allows for a new characterisation of the Weak topology…

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology,…

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple…

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic…

Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the matrix Schr\"odinger equation, is…

An extension of Riemmann's geometry into a direction dependent geometric structure is usually described by Finsler's geometry. Historically, this construction was motivated by the well-known Riemann's quartic length element example. Quite…