On Null Scrolls Satisfying the Condition $\Delta H = AH$

Commun. Korean Math. Soc. 2000 Vol. 15, No. 3, 533-540

Jin Suk Pak, Dae Won Yoon Kyungpook National University, Kyungpook National University

Abstract : In the present paper, we study a non-degenerate ruled surface along a null curve in a 3-dimensional Minkowski space $\Bbb E^3_1$, which is called a null scroll, and investigate some characterizations of null scrolls satisfying the condition $\Delta H= AH, A\in Mat(3,\Bbb R)$, where $\Delta $ denotes the Laplacian of the surface with respect to the induced metric, $H$ the mean curvature vector and $Mat(3,\Bbb R)$ the set of $3\times 3$-real matrices.

Keywords : null frame, null scroll, mean curvature vector, Minkowski space