arXiv research

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

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

Given a constant vector field $Z$ in Minkowski space, a timelike surface is said to have a canonical null direction with respect to $Z$ if the projection of $Z$ on the tangent space of the surface gives a lightlike vector field. In this paper we describe these surfaces in the ruled case. For example when the Minkowski …

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…

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…

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

New tractor geometry derived from asymptotically flat spacetimes.

Let $\widetilde{J}$ be the canonical para-complex structure on $\mathbb{R}^4$. In this paper we study $3$-dimensional centro-affine hypersurfaces with a $\widetilde{J}$-tangent centro-affine vector field (sometimes called $\widetilde{J}$-tangent centro-affine hypersurfaces) as well as $3$-dimensional $\widetilde{J}$-ta…

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 canonical curves and Kropina metrics in Lagrangian contact geometry.

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

Efficient inference for adaptive data with directional stability condition.

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

Let X be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): X and all its subvarieties are of general type and the canonical divisor K_X is ample at smooth points and Kawamata log terminal points of X, provided that K_X is Q-Cartier, no Calabi-Yau variety…

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null tangents or null normals) are obtained. The achieved results are illustrated by ex…

Let $\mathcal{H}$ denote the future outgoing null hypersurface emanating from a spacelike 2-sphere $S$ in a vacuum spacetime $(\mathcal{M},\mathbf{g})$. In this paper we study the so-called canonical foliation on $\mathcal{H}$ introduced by Klainerman and Nicolò and show that the corresponding geometry is controlled lo…

The paper proves asymptotic normality for multinomial logistic regression on null covariates.

This article is concerned with an observation for proving non-existence of canonical Kahler metrics. The idea is to use a rather explicit type of degeneration that applies in many situations. Namely, in a variation on a theme introduced by Ross-Thomas, we consider flops of the deformation to the normal cone. This yield…

This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] . x = 0, where x is an unknown n-dimensional real vector to be determined up to an overall norm…

This paper solves the structure of link concordance groups, proving they are infinitely generated.

Study of null φ-slant curves in specific 3D manifolds.

The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang find a sufficient condition for …

The paper examines asymptotic lines of plane fields in 3D space.

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.

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

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

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…

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

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…

In this article we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a generalisation of the tractor calculus of conformal manifolds adapted to the case of degene…

Study optimal transport on null hypersurfaces and null energy condition.

A new probabilistic polygonal curve representation using Gaussian Mixture Models.

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

Null Kähler metrics are characterized by Painlevé I or II ODEs.

In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique Frenet frame for which the original parameter is distinguished. Moreover, we obtain …

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…

Solves Einstein vacuum equations gluing problem for close Minkowski data.

This is an account of some aspects of the geometry of Kähler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kähler affine metrics of Yau's Schwarz lemma for volume forms. By a theorem of Chen…

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.

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 …

Classifies normal stable Horikawa surfaces with smoothable singularities.

New findings on how conformal rescalings affect spacetime metrics.

Rigging technique introduced in \cite{bi0} is a convenient way to address the study of null hypersurfaces. It offers in addition the extra benefit of inducing a Riemannian structure on the null hypersurface which is used to study geometric and topological properties on it. In this paper we develop this technique showin…

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistr…

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

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…

In this paper, we introduce canonical principal direction (CPD) submanifolds with higher codimension in Euclidean spaces. We obtain the complete classification of surfaces endowed with CPD in the Euclidean 4-space.