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

## TL;DR

This paper establishes conditions for the existence and uniqueness of minimal timelike strips in Lorentz-Minkowski space that contain a specified lightlike curve with a given normal bundle.

## Contribution

It provides necessary and sufficient conditions for constructing minimal timelike strips in Lorentz-Minkowski space with prescribed lightlike curves and normal bundles.

## Key findings

- Derived conditions for existence of minimal timelike strips.
- Proved uniqueness of solutions under certain conditions.
- Extended the Björling problem to lightlike curves in Lorentz-Minkowski space.

## Abstract

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.