LAUSR

Abstract In this paper, we consider spacelike and timelike surfaces satisfying an interesting geometric property that the gradient of the mean curvature is a principal direction in a Minkowski 3-space. It is proved that these surfaces are linear Weingarten and contain all biconservative surfaces in a Minkowski 3-space. We call them generalized biconservative surfaces (or GB surfaces in short). We give a complete explicit classification result of spacelike and timelike GB surfaces in Minkowski 3-space, respectively. Our results show that the non-CMC GB surfaces in Minkowski 3-space are locally either surfaces of revolution or null scrolls.