Geodesic
Non-degenerate surfaces of revolution in Minkowski space that satisfy the relation aH + bK = c
Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2 
R. López; Ö. Boyacioğlu Kalkan; D. Saglam. Non-degenerate surfaces of revolution  in Minkowski space that satisfy the relation aH + bK = c. Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a4/
@article{AMUC_2011_80_2_a4,
     author = {R. L\'opez and \"O. Boyacio\u{g}lu Kalkan and D. Saglam},
     title = {Non-degenerate surfaces of revolution  in {Minkowski} space that satisfy the relation {aH} + {bK} = c},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2011},
     volume = {80},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a4/}
}
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In this work we study spacelike and timelike surfaces of revolution in Minkowski space E 1 3 that satisfy the linear Weingarten relation aH + bK = c , where H and K denote the mean curvature and the Gauss curvature of the surface and a, b and c are constants. The classification depends on the causal character of the axis of revolution, We will give a first integral of the equation of the generating curve of the surface, obtaining explicit solutions for some particular choices of the constants a, b and c . Also, we completely solve the equation when the axis of revolution of the surface is lightlike.