Related papers: Blaschke's problem for timelike surfaces in pseudo…
Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
We introduce and study \emph{brachistochrone-ruled timelike surfaces} in Newtonian and relativistic spacetimes. Starting from the classical cycloidal brachistochrone in a constant gravitational field, we construct a Newtonian…
In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of…
Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair…
This paper contains some results about Teichm\"uller spaces of non-orientable surfaces (Klein surfaces). We prove several theorems giving isomorphisms between deformation spaces of Klein surfaces. These results show the similarity between…
This paper aims to study the relationship between the timelike extremal hypersurfaces and the classical minimal surfaces. This target also gives the long time dynamics of timelike extremal hypersurfaces in Minkowski spacetime…
We give a definition of isoclinic parametric surfaces in $\mathbb{R}^4_2$ and prove that such an isoclinic conformal immersion comes from two holomorphic functions. A Cauchy problem was proposed and solved, namely: construct an isoclinic…
A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first…
A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any…
The Bj\"orling problem and its solution is a well known result for minimal surfaces in Euclidean three-space. The minimal surface equation is similar to the Born-Infeld equation, which is naturally studied in physics. In this…
We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi…
We derive a correspondence between (Lorentzian) harmonic maps into the pseudosphere $S_1^2$, with appropriate regularity conditions, and certain connection 1-forms. To these harmonic maps, we associate a representation of type Weierstrass,…
We define the flatness and quasi-flatness problems in cosmological models. We seek solutions to both problems in homogeneous and isotropic Brans-Dicke cosmologies with varying speed of light. We formulate this theory and find perturbative,…
Timelike surfaces in the three-dimensional Heisenberg group with left invariant semi-Riemannian metric are studied. In particular, non-vertical timelike minimal surfaces are characterized by the non-conformal Lorentz harmonic maps into the…
We classify the volume preserving stable hypersurfaces in the real projective space $\mathbb{RP}^n$. As a consequence, the solutions of the isoperimetric problem are tubular neighborhoods of projective subspaces $\mathbb{RP}^k\subset…
Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike…
The singular Bj\" orling problem and its solution for timelike minimal surfaces is a well-known result in minimal surface theory. In this article, we give a different proof of this theorem using split-harmonic maps. This is motivated by a…
In this paper, we consider surfaces in 4--dimensional pseudo--Riemannian space--forms with index 2. First, we obtain some of geometrical properties of such surfaces considering their relative null space. Then, we get classifications of…
We review the similarity solutions proposed by Waylen for a regular time-dependent axisymmetric vacuum space-time, and show that the key equation introduced to solve the invariant surface conditions is related by a Baecklund transform to a…