4 citations · 14 across the 8 of their papers we have counts for
8 papers
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…
Sub-Lorentzian extremals defined by an antinorm
A. V. Podobryaev
We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra an…
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…
Attainable set for rank 3 step 2 free Carnot group with positive controls
A. V. Podobryaev
We find the attainable set for a control system on the free Carnot group of rank and step with positive controls. This kind of control systems is connected with the theory…
Homogeneous geodesics in sub-Riemannian geometry
A. V. Podobryaev
We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic t…
Casimir functions of free nilpotent Lie groups of steps three and four
Alexey V. Podobryaev
Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3, 4 and corresponding connected and simply connected Lie groups…