Mediterranean Journal of Mathematics vol:10 issue:2 pages:1035-1049
In this paper, we study surfaces in Lorentzian product spaces M2(c) × R1. We classify constant angle spacelike and timelike surfaces in S2 × R1 and H2 × R1. Moreover, complete classifications of spacelike surfaces in S2×R1 and H2×R1 and timelike surfaces in M2(c)×R1 with a canonical principal direction are obtained. Finally, a new characterization of the catenoid of the 3rd kind is established, as the only minimal timelike surface with a canonical principal direction in Minkowski 3-space.