arXiv subjects

Alexandre Lymberopoulos

Publications and source records attributed to Alexandre Lymberopoulos.

3 recordsLinked to original sources

arXiv2019

A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$

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 and minimal positive (negative) spacelike surface in $\mathbb{R}^4_2$, containing a given positive (negative) real analytic curve. At last, we study the important and well-known Bj\"orling problem, providing some examples was given in the last section.

math.DG↗

arXiv2019

On The Bj\"orling Problem For Lightlike Curves In $\mathbb{R}^4_1$

In this work we provide necessary and sufficient conditions for the existence of a minimal timelike strip in Lorentz-Minkowski space $\mathbb{R}^4_1$ containing a given lightlike curve and prescribed normal bundle. We also discuss uniqueness of solutions.

math.DG↗

arXiv2016

A local characterization for constant curvature metrics in 2-dimensional Lorentz manifolds

In this paper we define Fermi-type coordinates in a 2-dimensional Lorentz manifold, and use this coordinate system to provide a local characterization of constant Gaussian curvature metrics for such manifolds, following a classical result from Riemann. We then exhibit particular isometric immersions of such metrics in the pseudo-Riemannian ambients L^3 (i.e., usual Lorentz-Minkowski space) and R^3_2 (i.e., R^3 endowed with an index 2 flat metric).

math.DG↗