arXiv research

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.

Classified spaces in low dimensions.

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

Maximal surfaces in Lorentz-Minkowski space have conjugate graphs.

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

Unified estimates for mean curvature in Lorentz-Minkowski space.

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…

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…

The study uses isothermic coordinates to analyze space-like surfaces with constant curvature.

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

Constructs graphs with singularities in a special space.

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 …

The paper shows how null hypersurfaces behave in Lorentz-Minkowski space.

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

The paper proves a stability result for translating space-like graphs in Lorentz manifolds.

The paper studies Gauss maps of space-like stationary surfaces in Lorentz-Minkowski space, focusing on ramification and unicity.

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

Study surfaces with nonvanishing Gauss curvature in Lorentz-Minkowski space.

In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with $P+aH=b$ in a locally symmetric Lorentz space $L_{1}^{n+1}$. Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces $L_{1}^{n+1}$ satisfying some curvature conditions…

Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.

New examples of mixed-type zero-curvature graphs found.

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.

New approach classifies rotational Weingarten surfaces in Lorentz-Minkowski space.

We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the …

Extends Newton's minimal resistance problem to Lorentz-Minkowski space.

We study the third Laplace-Beltrami operator of timelike rotational surface of (T,L)-type in three dimensional Lorentz-Minkowski space.

Classifies zero mean curvature surfaces in Lorentz-Minkowski space.

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

The paper classifies maximal translation surfaces in Lorentz-Minkowski space.

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.

Paper connects surfaces in 4D and 3D spacetime.

The paper classifies ruled surfaces in a specific space that move in a special way.

Geodesic orbit property studied for Lorentz manifolds.

We introduce a new approach to the study of timelike minimal surfaces in the Lorentz-Minkowski space through a split-complex representation formula for this kind of surface. As applications, we solve the Björling problem for timelike surfaces and obtain interesting examples and related results. Using the Björling repre…

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 review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

Navigation in Lorentz Finsler geometry induces isoparametric hypersurfaces.

The paper classifies ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia.

Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.

We construct triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space, with the same topology as the triply periodic minimal surfaces in the Euclidean 3-space, called Schwarz rPD surfaces.

We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.

We investigate a variational problem in the Lorentz-Minkowski space $ł^3$ whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a plana…

In this paper we study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due to the presence of a closed conformal vector field. More precisely, we begin by extending to these spaces a result of J. Simons on the minimality of cones in Euclidean space, and apply…

In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper's surface among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in the Lorentz-Minkowski space L3.

Study modular surfaces in Lorentz-Minkowski 3-space, classifying and analyzing their curvature and applications.

Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.

Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.