부산대학교 도서관

It is well known that the only surfaces $S$ in $\Bbb{R}^3$ whose Gauss curvature $K$ and mean curvature $H$ satisfy $H^2=K$ are open pieces of planes or spheres. In the paper under review, the authors consider the same condition for the case in which $S$ is a Lorentzian surface in $\Bbb{L}^3$, and obtain the following local classification: up to the trivial cases (plane and sphere), the $B$-scrolls and null scrolls with minimal polynomial of the shape operator ${(t-b)}^2$, $b\not={\rm constant}$, are the only Lorentzian surfaces satisfying $H^2=K$.