arXiv research

In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…

4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which are called the null strings. Properties of congruences (foliations) o…

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

Defines null G-structures on Lorentzian manifolds and explores their symmetries.

In the Compressed Sensing community, it is well known that given a matrix $X \in \mathbb R^{n\times p}$ with $\ell_2$ normalized columns, the Restricted Isometry Property (RIP) implies the Null Space Property (NSP). It is also well known that a small Coherence $μ$ implies a weak RIP, i.e. the singular values of $X_T$ l…

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 …

Integrable flows on null curves in anti-de Sitter 3-space studied.

Study on null helices in semi-Riemannian manifolds with special submanifolds.

New concepts of barriers and black regions defined for Lorentzian manifolds.

Null distance metric studies spacetime convergence.

Study on null-projectability of Levi-Civita connections in neutral metrics.

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a nul…

Constructs Lorentzian harmonic maps and associated timelike surfaces.

Synthetic framework for null hypersurfaces in non-smooth spacetimes.

The paper studies convergence of cosmological spacetimes using null distance.

The paper extends spacetime topology results using codimension 2 null cut locus properties.

Study shows knots with specific properties avoid certain topological surgeries.

The study classifies quasi-minimal surfaces in 4D pseudo-Riemannian space-forms with positive nullity.

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

Study of hypersurfaces with specific expansion properties.

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). Using an algebraic classification of pseudo-Riemannian spaces in terms of the boost-weight decomposition we first show more generally that a space which is not characterise…

Study optimal transport on null hypersurfaces and null energy condition.

Study null hypersurfaces in Lorentzian manifolds, proving Riemannian flow structure.

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…

Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop-Gromov relative volu…

Study on almost Robinson geometries, focusing on their intrinsic torsion and leaf space properties.

New types of null hypersurfaces found in Sasakian space-forms.

Study invariants of null-homologous knots in thickened surfaces.

The paper studies marginally trapped submanifolds in Lorentzian manifolds under null energy condition.

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface $Ω$ extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawki…

The study connects electromagnetic structures to Legendrian fields on the 3-sphere.

Study extends null distance concept to Lorentzian length spaces for spacetime analysis.

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

We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$ terminates at past null infinity $\mathcal{I}^-$ and $\mathcal{S}_0:=\partial\underline{\mathcal{N}}_0$…

We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions.

Geometric transformations on null curves in AdS induce KdV solutions.

Paper finds space-like maximal surfaces with entire null lines in 3D space-time.

Study on null curves in Klein's quartic moduli space.

Study reveals hidden null components in overparametrized neural networks.

Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.

Note shows equivalence of recent NEC reformulation to classical NEC for $C^2$-metrics.

Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.

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

The Hopf invariant is linked to null-homotopy properties of maps.

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dime…

Study shows knot grading properties in specific spaces.

We consider polyhedra and 4-polytopes in Minkowski spacetime - in particular, null polyhedra with zero volume, and 4-polytopes that have such polyhedra as their hyperfaces. We present the basic properties of several classes of null-faced 4-polytopes: 4-simplices, "tetrahedral diamonds" and 4-parallelotopes. We propose …