arXiv research

A new flow method reduces Lorentz contraction to a simple algebraic decay.

Study of magnetic geodesics on Heisenberg nilmanifolds.

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the produc…

Refines d'Alembertian for signed Lorentz distance functions in metric measure spacetimes.

The paper proves properties of Lipschitz spacetimes with bounded Ricci curvature.

This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of conformal invariant pseudodifferential operators are linear combinations of Weyl con…

We study conformal Fefferman-Lorentz manifolds introduced by Fefferman. To do so, we introduce Fefferman-Lorentz structure on (2n+2)-dimensional manifolds. By using causal conformal vector fields preserving that structure, we shall establish two theorems on compact Fefferman-Lorentz manifolds: One is the coincidence of…

Study shows compact Lorentz manifolds can't have closed geodesics.

This is Part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in Part I, a compactification of these isometry groups, and called ``bi-polarized'' those Lorentz manifolds having a ``trivial '' compactification. Here we show a geometric rigidity of non-bi-polarized Lorentz manifolds; …

The study introduces canonical coordinates for Lorentz surfaces and proves a Bonnet-type theorem.

LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

A world sheet in Lorentz-Minkowski space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds in Lorentz-Minkowski space. In this paper we investigate differential geometry of world sheets in Lorentz-Minkowski space as an application of the theory of big wave fronts.

Study on maximal surfaces with high genus in Lorentz-Minkowski space.

Defines and computes a generalized spectral action for Lorentz warped products.

We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.

The three-dimensional Heisenberg group $H_3$ has three left-invariant Lorentz metrics $g_1$, $g_2$ and $g_3$. They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric $g_1$ as a Lorentz Ricci soliton. This Ricci soliton $g_1$ is a shrinking non-gradient Ricci soliton. Likew…

Classified spaces in low dimensions.

The paper explores unique properties of Darboux transformations of spacelike curves in the Lorentz-Minkowski plane.

A condition of Osserman type, called $φ$-null Osserman condition, is introduced and studied in the context of Lorentz globally framed $f$-manifolds. An explicit example shows the naturalness of this condition in the setting of Lorentz $\mathcal{S}$-manifolds. We prove that a Lorentz $\mathcal{S}$-manifold with constant…

We classify isometries of compact Lorentz manifolds.

This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially Lorentz transformations. In particular we show how this is related to geodesic fol…

Lorentz-Finsler geometry reveals new and old inequalities.

The paper examines Lorentz Ricci solitons on specific Lie groups.

Maximal surfaces in Lorentz-Minkowski space have conjugate graphs.

Unified estimates for mean curvature in Lorentz-Minkowski space.

Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of São Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_ν$, with focus on Lorentz-Minkowski space and its role in Physics; (ii) a version of the Funda…

We study minimal Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric whose first normal space is two-dimensional and whose Gauss curvature $K$ and normal curvature $\varkappa$ satisfy the inequality $K^2-\varkappa^2 >0$. Such surfaces we call minimal Lorentz surfaces of general type. On any surface of …

We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.

We study proper, isometric actions of nonsolvable discrete groups Gamma on the 3-dimensional Minkowski space R^{2,1} as limits of actions on the 3-dimensional anti-de Sitter space AdS^3. To each such action is associated a deformation of a hyperbolic surface group Gamma_0 inside O(2,1). When Gamma_0 is convex cocompact…

Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.

Unified geometry for relativity and beyond.

Study geodesic orbit Lorentz nilmanifolds, proving structural properties.

Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far very few results on minimal Lorentz surfaces in indefinite space forms are know…

The paper studies magnetic curvature and proves the existence of closed orbits on low energy levels.

New inequality shows all special submanifolds in light cone are totally umbilical spheres.

Paper connects surfaces in 4D and 3D spacetime.

Study of Gödel Universe as Lie group with specific metric.

Paper solves Hessian quotient equations in Lorentz-Minkowski space with Dirichlet boundary conditions.

L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.

A new model uses Lorentz-Finsler geometry to predict wave propagation.

Navigation in Lorentz Finsler geometry induces isoparametric hypersurfaces.

A Lorentz surface in the four-dimensional pseudo-Euclidean space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. In the present paper we obtain the complete classification of quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.

The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativist…

We study Lorentz hypersurfaces $M_{1}^{n}$ in $E_{1}^{n+1}$ satisfying $\triangle \vec {H}= α\vec {H}$ with non diagonal shape operator, having complex eigenvalues. We prove that every such Lorentz hypersurface in $E_{1}^{n+1}$ having at most five distinct principal curvatures has constant mean curvature.

Paper classifies ruled surfaces in Lorentz-Minkowski space for a specific flow.

Constructs graphs with singularities in a special space.

The paper studies helicoidal surfaces of non-lightlike frontals in Lorentz-Minkowski 3-space.