Streamlines of perfect fluid as geodesics in Riemannian space-time

Geodesics on non-Riemannian Geometric theory of Planar Defects

The method of Hamilton-Jacobi is used to obtain geodesics around non- Riemannian planar torsional defects.It is shown that by perturbation expansion in the Cartan torsion the geodesics obtained are parabolic curves along the plane x-z when the wall is located at the plane x-y.In the absence of defects the geodesics reduce to straight lines.The family of parabolas depend on the torsion parameter and describe a gravitationally repulsive domain wall.Torsion here plays the role of the Burgers vector in solid state physics.

类时与零时空测地线的黎曼几何方法

A Riemannian geometric approach for timelike and null spacetime geodesics

提出通过将洛伦兹度量投影到Killing向量方向获得广义Jacobi度量的方法，证明其继承原时空测地线，并可用于研究强宇宙审查猜想的破坏。

Hydrodynamic Flow as Congruence of Geodesic Lines in Riemannian Space-Time

It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.

Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry. The progress in the last two decades has become impressive, being especially relevant the systematic introduction of (infinite-dimensional) variational methods. Our purpose is to give an overview, from refinements of classical results to updated variational settings. First, several properties (and especially completeness) of geodesics in some ambient spaces…

A Riemannian approach to Randers geodesics

In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents itself in the characterisation of geodesics in Randers spaces of constant flag curvature. To achieve a simple, Riemannian derivation of this special family of curves, we exploit the connection between Randers spaces and the Zermelo problem of time-optimal navigation in the presence of background fields. The characterisation of geodesics is then proven by generalising an intuitive argument developed recently for the sol…