Streamlines of a perfect fluid as geodesics in Riemannian space-time

Instability of Periodic Streamlines in a Perfect Fluid

We show that any stationary solution to the n-dimensional Euler equations is linearly unstable in the norm of H(Ω), for any s 6= 1 n−1 , if it possesses a locally non-isochronous periodic streamline. The proof uses the technique of linear geometric optics.

A rotating incompressible perfect fluid space - time

A rigidly rotating incompressible perfect fluid solution of Einstein’s gravitational equations is given. The Petrov type is D, and the metric admits a fourparameter isometry group. The Gaussian curvature of the instantaneous constantpressure surfaces is positive and they have two ring-shaped cusps. PACS numbers: 04.20.Cv, 04.20.Jb, 04.40.Dg, 97.60.-s Submitted to: Class. Quantum Grav. Rotating ...

Closed Geodesics in Compact Riemannian Good Orbifolds and Horizontal Periodic Geodesics of Riemannian Foliations

In this paper we prove the existence of closed geodesics in certain types of compact Riemannian good orbifolds. This gives us an elementary alternative proof of a result due to Guruprasad and Haefliger. In addition, we prove some results about horizontal periodic geodesics of Riemannian foliations and stress the relation between them and closed geodesics in Riemannian orbifolds. In particular w...

Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

Computing Geodesics on a Riemannian Manifold