In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...

There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization, and the analogous definitions for normed spaces represent a promising topic. An example is the geometry of simplices in non-Euclidean normed spaces. We pres...

Some examples of the interplay between matrix theory, graph theory and n-dimensional Euclidean geometry are presented. In particular, qualitative properties of interior angles in simplices are completely characterized. For right simplices, a relationship between the tree of legs and the circumscribed Steiner ellipsoids is proved.

Some examples of the interplay between matrix theory, graph theory and n-dimensional Euclidean geometry are presented. In particular, qualitative properties of interior angles in simplices are completely characterized. For right simplices, a relationship between the tree of legs and the circumscribed Steiner ellipsoids is proved.