相关论文: Geodesics on metrics of self-dual Taub-Nut type
Geodesic equations are solved when at least two of $\theta$, $\phi$ and $\psi$ are constant, or $r$ is constant, on scalar flat metrics of Eguchi-Hanson type. They can also be solved also on Eguchi-Hanson metrics which are Ricci flat if…
The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential…
An important aspect of General Relativity is to study properties of geodesics. A useful tool for describing geodesic behavior is the geodesic deviation equation. It allows to describe the tidal properties of gravitating objects through the…
We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain smallness assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is…
We show that if two 4-dimensional metrics of arbitrary signature on one manifold are geodesically equivalent (i.e., have the same geodesics considered as unparameterized curves) and are solutions of the Einstein field equation with the same…
We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the…
Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be…
The geodesic motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space is analysed. The generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions…
A class of generalized Taub-NUT gravitational instantons is reported in five - dimensional Einstein gravity coupled to a non-linear sigma model. The geodesic dynamics of a spinless particle of unit mass on these static gravitational…
The geodesic deviation equation has been investigated in the framework of $f(T,\mathcal{T})$ gravity, where $T$ denotes the torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor, respectively. The FRW metric is assumed and…
When graviton loops are taken into account, the background metric obtained as a solution to the one-loop corrected Einstein equations turns out to be gauge fixing dependent. Therefore it is of no physical relevance. Instead we consider a…
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…
We solve explicitly the geodesic equation for a wide class of (pseudo)-Riemannian homogeneous manifolds (G/H,m), including those with G compact, as well as non-compact semisimple Lie groups, under a simple algebraic condition for the metric…
Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system…
The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume…
This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…
A naturally parameterised curve in a Lie group with a left invariant metric is a geodesic, if its tangent vector left-translated to the identity satisfies the Euler equation $\dot{Y}=\operatorname{ad}^t_YY$ on the Lie algebra $\mathfrak{g}$…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal…
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…