Linear Weingarten surfaces foliated by circles in Minkowski space

TL;DR

This paper classifies spacelike surfaces in Minkowski space foliated by circles that satisfy a linear relation between mean and Gauss curvature, showing they are either surfaces of revolution or have constant curvature.

Contribution

It provides a complete classification of linear Weingarten surfaces foliated by circles in Minkowski space, identifying their geometric types.

Findings

Surfaces are either surfaces of revolution or have constant mean or Gauss curvature.

Classifies all such surfaces satisfying the linear Weingarten condition.

Shows these surfaces are characterized by specific curvature properties.

Abstract

In this work, we study spacelike surfaces in Minkowski space $E_1^3$ foliated by pieces of circles and that satisfy a linear Weingarten condition of type $a H+b K=c$, where $a,b$ and $c$ are constant and $H$ and $K$ denote the mean curvature and the Gauss curvature respectively. We show that such surfaces must be surfaces of revolution or surfaces with constant mean curvature H=0 or surfaces with constant Gauss curvature K=0.