A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Two flat sub-Lorentzian problems on Martinet distribution differ in attainable set intersections.
Researchers found the longest arcs for specific sub-Lorentzian structures.
Optimal transport explored on a specific geometric space.
Proves existence of longest paths in sub-Lorentzian problems.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
Study on surfaces in Heisenberg group with constant mean curvature.
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzi…
Researchers found sub-Lorentzian geodesics on a specific Lie subgroup.
We provide a classification of -invariant sub-Lorentzian structures on dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.
Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.
We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both $\SU(1,1)$ and $\CSU(1,1)$, connecting two fixed points. In particular, we prove that …
Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalisation of the la…
Study on Hausdorff dimension and curvature bounds in sub-Lorentzian Heisenberg group.
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which…
This paper classifies holonomy groups of K-contact sub-pseudo-Riemannian manifolds.
We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain e…
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike norma…
We consider the four-dimensional nonholonomic distribution defined by the 4-potential of the electromagnetic field on the manifold. This distribution has a metric tensor with the Lorentzian signature , therefore, the causal structure appears as in the general relativity theory. By means of the Pontryagin's m…