Non-degenerate surfaces of revolution in Minkowski space that satisfy the relation aH+bK=c

Abstract

In this work we study spacelike and timelike surfaces of revolution in Minkowski space E<inf>1</inf>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.