arXiv research

The study characterizes and analyzes spacelike surfaces with a canonical normal null direction in Minkowski 4-space.

The paper describes timelike surfaces with a canonical null direction in Minkowski space.

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

The paper classifies 3D hypersurfaces with specific geometric properties.

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual comp…

Researchers compute contact structures for null geodesics on specific spacetimes.

This paper proves a canonical foliation on null infinity for Kerr-like black holes.

Study of null hypersurface foliation in low regularity spacetimes.

Study canonical curves and Kropina metrics in Lagrangian contact geometry.

ZDP detects drift in large language models without labels, proving key theorems and metrics.

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

Solves natural PDEs for minimal Lorentz surfaces in 4D spacetime.

New tractor geometry derived from asymptotically flat spacetimes.

Study shows contact structure on null geodesic space for specific spacetimes.

A function that optimally aligns a timelike vector field with its gradients

In this paper we exploit the ideas and formalisms of twistor theory, to show how, on Minkowski space, given a null solution of the wave equation, there are precisely two null directions in $\ker df$, at least one of which is a shear-free ray congruence.

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of…

Null Lagrangian-preserving surgeries are a generalization of the Garoufalidis and Rozansky null-moves, that these authors introduced to study the Kricker lift of the Kontsevich integral, in the setting of pairs (M,K) composed of a rational homology sphere M and a null-homologous knot K in M. They are defined as replace…

This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null boundaries that arise from canonical 3- and 4-dimensional settings. A null hypersurf…

Study optimal transport on null hypersurfaces and null energy condition.

Classifies surfaces with a special direction in 4D space.

The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.

A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the n…

Defines Lorentzian angles for null vectors in geometry.

Solves Einstein vacuum equations gluing problem for close Minkowski data.

Researchers solved Einstein-Yang-Mills equations for arbitrary gauge groups.

We consider smooth plane curves which are convex with respect to the origin. We describe centro-affine invariants (that is, GL_+(2,R)-invariants), such as centro-affine curvature and arc length, in terms of the canonical Lorentz structure on the three dimensional space of all the ellipses centered at zero, by means of …

In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.

New findings on how conformal rescalings affect spacetime metrics.

Study characterizes hypersurfaces in product spaces with a canonical direction.

Study of $\alpha$-associated metrics on null hypersurfaces.

Study timelike bounce in charged null dust collapse, identifying key surfaces.

Survey on geometric, analytic, and topological aspects of 4D equations.

Study null geodesics on specific spacetimes, finding contact manifolds and Engel geometry applications.

Simplified proof of cosmic singularity theorem using new mathematical techniques.

Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful charac…

Proves compact Cauchy horizons have constant surface gravity under null energy condition.

There is a class of Laplacian like conformally invariant differential operators on differential forms $L^\ell_k$ which may be considered the generalisation to differential forms of the conformally invariant powers of the Laplacian known as the Paneitz and GJMS operators. On conformally Einstein manifolds we give explic…

Null distance encodes causal structure in spacetimes.

In the present paper we classify all surfaces in $\E^3$ with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.

In this paper we characterize and classify surfaces in ${\mathbb{H}}^2\times{\mathbb{R}}$ which have a canonical principal direction. Here ${\mathbb{H}}^2$ denotes the hyperbolic plane. We study some geometric properties such as minimality and flatness. Some examples are given to complete the study.

Null-Calibrated Conformal Selection via Target-Membership Scores

New contact structures extend supergravity solutions.

Study embeddings of free group products into automorphism groups.

Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vec…

Given a time function $τ$ on a spacetime $M$, we define a `null distance function', $\hat{d}_τ$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla τ$, we show that 1) $\hat{d}_τ$ is a definite distance function, which induces the manifold topology, 2) the causal struct…

A debiased score test detects linear structure in semiparametric models.

New approach constructs symplectic structure on pseudo-Riemannian geodesics.