Pseudo-Riemannian universe from Euclidean bulk

Spaces of pseudo-Riemannian geodesics and pseudo-Euclidean billiards

Many classical facts in Riemannian geometry have their pseudoRiemannian analogs. For instance, 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. We discuss the geometry of these structures in detail, as well as introduce an...

Spaces of pseudo - Riemannian geodesics and pseudo - Euclidean billiards Boris

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...

Semi-slant Pseudo-riemannian Submersions from Indefinite Almost Contact 3-structure Manifolds onto Pseudo-riemannian Manifolds

In this paper, we introduce the notion of a semi-slant pseudoRiemannian submersion from an indefinite almost contact 3-structure manifold onto a pseudo-Riemannian manifold. We investigate the geometry of foliations determined by horizontal and vertical distributions and provide a non-trivial example. We also find a necessary and sufficient condition for a semi-slant submersion to be totally geo...

Fractional Unstable Euclidean Universe

Despite common acceptance of Big Bang hypothesis among most cosmologists, nonetheless there are criticisms from a small number of theorists partly supported by astronomy observation suggesting that redshift data could not always be attributed to cosmological expansion. In this paper, a new approach to cosmology “fractional calculus” has been developed that we hope will attract attention from as...

1 Pseudo - Riemannian Geometry