Related papers: On timelike Bonnet surfaces in Lorentzian 3-manifo…

This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic…

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the…

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contraction property. The remarkable class of examples of spacetimes…

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane…

If an $m+2$-manifold $M$ is locally modeled on $\RR^{m+2}$ with coordinate changes lying in the subgroup $G=\RR^{m+2}\rtimes ({\rO}(m+1,1)\times \RR^+)$ of the affine group ${\rA}(m+2)$, then $M$ is said to be a \emph{Lorentzian similarity…

Bonnet has characterized his surfaces by a geometric condition. What is done here is a characterization of the same surfaces by two analytic conditions: (i) the mean curvature $H$ of a surface in $\mathbb{R}^3$ should admit a reduction to…

In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an…

We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics transverse to the foliation. In order to develop the necessary…

In this note, we use isothermic coordinate systems to explore global properties of space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.

We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with $\Lambda >0$ and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive…

We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and…

In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical…

We introduce a notion of Lorentzian metric space which drops the boundedness condition from our previous work and argue that the properties defining our spaces are minimal. In fact, they are defined by three conditions given by (a) the…

In this work, we prove the following three rigidity results: (i) in a real-analytic globally hyperbolic spacetime $(M,g)$ without boundary, the time separation function restricted to a thin exterior layer of a unknown compact subset $K…

We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any timelike curvature bound, either from above or below, and…

Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.

We solve the Bonnet problem for surfaces in the homogeneous 3-manifolds with a 4-dimensional isometry group. More specifically, we show that a simply connected real analytic surface in H^2xR or S^2xR is uniquely determined pointwise by its…

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I_{p}^{3} that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron in order for…

The paper generalizes some of the well-known results for K3 surfaces to higher-dimensional irreducible symplectic (or, equivalently, compact irreducible hyperkaehler) manifolds. In particular, we discuss the projectivity of such manifolds…