On minimal surfaces immersed in three dimensional Kropina Minkowski space

TL;DR

This paper derives a PDE characterizing minimal surfaces in three-dimensional Kropina Minkowski space and investigates specific cases, including minimal translation surfaces, concluding that the plane is the unique such surface.

Contribution

It introduces a PDE for minimal surfaces in Kropina Minkowski space and characterizes minimal translation surfaces, establishing the plane as the only example.

Findings

Derived the PDE for minimal surfaces in Kropina Minkowski space

Characterized minimal translation surfaces in this setting

Proved the plane is the only minimal translation surface

Abstract

In this paper we consider a three dimensional Kropina space and obtain the partial differential equation that characterizes a minimal surfaces with the induced metric. Using this characterization equation we study various immersions of minimal surfaces. In particular, we obtain the partial differential equation that characterizes the minimal translation surfaces and show that the plane is the only such surface.