# Riemann Zero Mean Curvature Examples in Lorentz-Minkowski Space

## TL;DR

This paper explores zero mean curvature surfaces in Lorentz-Minkowski space, focusing on those foliated by circles in parallel planes, revealing new geometric features distinct from Euclidean cases.

## Contribution

It provides a detailed geometric description of Riemann zero mean curvature surfaces in Lorentz-Minkowski space with circles in spacelike and timelike planes, highlighting novel features.

## Key findings

- Surfaces foliated by circles in Lorentz-Minkowski space exhibit unique geometric properties.
- Distinct behaviors are observed depending on whether circles lie in spacelike or timelike planes.
- The study expands understanding of zero mean curvature surfaces beyond Euclidean geometry.

## Abstract

Riemann zero mean curvature examples in the Lorentz-Minkowski space are surfaces with zero mean curvature foliated by circles contained in parallel planes. In contrast to the Euclidean case, this family of surfaces presents new and rich features because of the variety of types of circles. In this paper, we give a geometric description of these examples when the circles are contained in spacelike planes and timelike planes.