Let H be the hyperbolic space of dimension n + 1. A geodesic foliation of H is given by a smooth unit vector field on L all of whose integral curves are geodesics. Each geodesic foliation of L determines an n-dimensional ...

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 ...

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance ...

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are ...

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are ...

Type A surfaces are the locally homogeneous affine surfaces which can be locally described by constant Christoffel symbols. We address the issue of the geodesic completeness of these surfaces: we show that some models for ...

A pair (P,Q) of orthogonal projections in a Hilbert space H is called a Fredholm pair if QP:R(P)→R(Q)is a Fredholm operator. Let F be the set of all Fredholm pairs. A pair is called compact if P−Q is compact. Let C be the ...

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 ...