Related papers: Geodesics on an ellipsoid in Minkowski space
Riemann zero mean curvature examples in the Lorentz-Minkowski space are surfaces with zero mean curvature foliated by circles contained in parallel planes. In contrast to the Euclidean case, this family of surfaces presents new and rich…
In the present paper, we obtain explicit formulae for geodesics in some left-invariant sub-Finsler problems on Heisenberg groups $\mathbb{H}_{2n+1}$. Our main assumption is the following: the compact convex set of unit velocities at…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all…
In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichm\"uller geodesic trajectories.The main tool is quantitative nondivergence of…
In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new…
A generalisation of Riemannian geometry is considered, based exclusively on the minimal assumptions that the line element $ds$ is a regular function of position and direction and that the distance of every point from itself is equal to…
It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of…
We construct a counterexample to a conjectured inequality L<2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem…
A technique for generating spherically symmetric dislocation solutions of a direct Poincar\'{e} gauge theory of gravity based on homogeneous functions which makes Cartan torsion to vanish is presented.Static space supported dislocation and…
Geodesics on Riemannian manifolds are precisely the locally length-minimizing curves, but their explicit description via simple functions is rarely possible. Geodesics of the simplest form, such as lines on Euclidean space and great circles…
A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and…
It is shown that the Jacobi problem of geodesics on ellipsoid may be reduced to more simple one, namely to the special case of the Clebsch problem. The last one may be solved directly by using Weber's approach in terms of multi-dimensional…
A semi-Riemannian manifold is said to satisfy $R\ge K$ (or $R\le K$) if spacelike sectional curvatures are $\ge K$ and timelike ones are $\le K$ (or the reverse). Such spaces are abundant, as warped product constructions show; they include,…
We investigate here all the possible invariant metric functions under the action of various kinds of semi-direct product Poincar\'e subgroups and their deformed partners. The investigation exhausts the possible theoretical frameworks for…
Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of…
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data…
We study the motion of particles in the background of a scalar-tensor theory of gravity in which the scalar field is kinetically coupled to the Einstein tensor and we present the null geodesic structure for asymptotically flat, AdS, and dS…
We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ as found in [Ayon-Beato E., Garbarz A., Giribet G. and…
A simple differential analysis of issue of the correspondence between notion of geodesics in gravitation theory of GTR and straights of inertial motion in the Minkowski space-time discovers that, conventional certification of the geodesics…