We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on ...

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural ...

In this paper westudy the metric tensor of a homogeneous, isotropic, 5-dimensional pseudo Riemannian space, solving the corresponding Einstein equations when the spatial component is flat, spherical or pseudo spherical

This work concerns the invariant Lorentzian metrics on the Heisenberg Lie group of dimension three H3(R) and the bi-invariant metrics on the solvable Lie groups of dimension four. We start with the indecomposable Lie groups ...

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors ...

Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space ...

The goal of this work is to study the geometric conditions required on a pseudo-Riemannian manifold M to guarantee the existence of solutions of a second order partial differential equation posed on M. We closely follow ...

We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical ...

Apresentaremos uma demonstração para o célebre teorema de Mergulho de Nash, que afirma de toda variedade riemanniana compacta pode ser mergulhada isométricamente em algum espaço elucidado. A ideia central na demonstração ...

Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical ...