4 papers · 1 filter
Cut loci and diameters of the Berger lens spaces
Alexey Podobryaev
In this paper, we study Riemannian metrics on the three-dimensional lens spaces that are deformations of the standard Riemannian metric along the fibers of the Hopf fibration. In o…
One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R)
A. V. Podobryaev
We consider a one-parametric series of left-invariant Lorentzian structures on the universal covering of the Lie group SL(2,R). These structures have SO(1,1)-symmetry and they are…
Cut loci of Berger type Lorentzian structures
A. V. Podobryaev
Consider the deformation of the standard Lorentzian metric on the anti de-Sitter space along the fibers of the Hopf fibration. We study the universal covering of this Lorentzian ma…
Existence theorem for sub-Lorentzian problems
L. V. Lokutsievskiy, A. V. Podobryaev
In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We…