LINEAR WEINGARTEN SURFACES FOLIATED BY CIRCLES IN MINKOWSKI SPACE

Abstract

In this work, we study spacelike surfaces in Minkowski space ${\bf E}_1^3$ foliated by pieces of circles that satisfy a linear Weingarten condition of type $aH + bK = c$, where $a,b$ and $c$ are constants 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 $K=0$.