A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in $\mathbb{H}^2\times \mathbb{R}$

TL;DR

This paper establishes a geometric link between maximal surfaces in anti-De Sitter space-time and minimal surfaces in hyperbolic plane times real line, providing new examples to illustrate the correspondence.

Contribution

It introduces a novel geometric correspondence between two classes of surfaces in different spaces and constructs new examples of maximal surfaces in anti-De Sitter space-time.

Findings

Established a correspondence between maximal and minimal surfaces.

Constructed new examples of maximal surfaces in anti-De Sitter space.

Illustrated the correspondence with explicit examples.

Abstract

A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in the Riemannian product of the hyperbolic plane and the real line is established. New examples of maximal surfaces in anti-De Sitter space-time are obtained in order to illustrate this correspondence.