arXiv research

Study explores solvable Lie groups' actions on closed Lorentzian manifolds.

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some n…

New method finds closed timelike geodesics on Lorentzian manifolds.

Compact group found for special Lorentzian manifolds.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

We give a new existence proof for closed hypersurfaces of prescribed mean curvature in Lorentzian manifolds.

I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume element, some information on the topology and metric is encoded in the partial or…

The existence of closed hypersurfaces of prescribed curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.

New connections found with specific torsion properties.

The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

3D Lorentzian manifolds can't be closed Einstein with positive constant.

Classifies specific types of Lorentzian manifolds with unipotent holonomy.

We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations. Besides we provide an example of a Lorentzian foliation on a compact 3-manifold which…

We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\Sl(2, \C)$-Lorentzian co…

Study of recurrent Lorentzian Weyl spaces with detailed local and global structures.

A Sim(n-1,1) affine manifold is an affine manifold whose linear holonomy is contained in the similarity lorentzian group but not in the lorentzian group. The class of similarity lorentzian affine manifolds is a small part in the nice class of conformally lorentzian flat manifolds. In this paper we show that a compact S…

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, …

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

In this work we investigate families of compact Lorentzian manifolds in dimension four. We show that every lightlike geodesic on such spaces is periodic, while there are closed and non-closed spacelike and timelike geodesics. Their isometry groups are computed. We also show that there is a non trivial action by isometr…

Following the lines of a celebrated result by R. Bott (Comm. Pure Appl. Math. 9, 1956) we study the Morse index of the iterated of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic $γ$, w…

The paper examines timelike conformal fields on 3-manifolds and finds they are rigidly tied to specific geometric structures.

We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed geodesics to the causal structure of the surface and the homotopy type of the Lorentzian metric.

Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…

Smoothly approximates embeddings in Lorentzian manifolds.

Modeling wormhole creation without singularities in relativity.

Proves metrics of curvature ≤ -1 on surfaces are isometric to space-like convex surfaces in anti-de Sitter space.

Defines Lorentzian distance on contactomorphisms, proving continuity and finite conditions.

Novel contact metric structures lead to supergravity solutions.

Because no closed timelike curve (CTC) on a Lorentzian manifold can be deformed to a point, any such manifold containing a CTC must have a topological feature, to be called a timelike wormhole, that prevents the CTC from being deformed to a point. If all wormholes have horizons, which typically seems to be the case in …

Local Lorentzian theorem preserves metrics or makes them flat.

Study establishes time functions in Lorentzian spaces without requiring manifold structure.

A Lorentzian manifold is defined here as a smooth pseudo-Riemannian manifold with a metric tensor of signature ((2n +1, 1)). A Robinson manifold is a Lorentzian manifold (M) of dimension (\geqslant 4) with a subbundle (N) of the complexification of (TM) such that the fibers of (N\to M) are maximal totally null (isotrop…

Given a Lorentzian manifold $(M,g_L)$ and a timelike unitary vector field $E$, we can construct the Riemannian metric $g_R=g_L+2ω\otimesω$, being $ω$ the metrically equivalent one form to $E$. We relate the curvature of both metrics, especially in the case of $E$ being Killing or closed, and we use the relations obtain…

Classifies manifolds with specific spinors and constructs parallel spinors.

Clarifies definitions of global hyperbolicity in various spaces.

We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.

The study confirms essential self-adjointness for certain differential operators on manifolds.

It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the classification of two-symmetric Lorentzian manifolds is explained; conformally …

Finds a limit on Lorentzian manifolds.

Researchers generalize space forms in Riemannian geometry using specific vector fields.

A flat complete causal Lorentzian manifold is called {\it strictly causal} if the past and the future of each its point are closed near this point. We consider strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the con…

Diagonalizes metrics of 3D Lorentzian manifolds.

Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.

Study proves 3-manifolds with parallel vector fields have odd Betti numbers.

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…

Study geodesics on compact Lorentzian solvmanifolds, finding conditions for closedness.

We study the motion of an $n$-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power $p$ of the mean curvature. We prove that for any $p\in (0,1]$, the flow exists for all time when the Ricci tensor of the ambient s…