Vol. LXXX, 2 (2011)
p. 201 - 212

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

R. López, Ö. Boyacioğlu Kalkan, D. Saglam

Received: April 19, 2010;   Revised: July 1, 2011;   Accepted: April 14, 2011

Abstract.   In this work we study spacelike and timelike surfaces of revolution in Minkowski space E13 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.

Keywords:  Minkowski space; surface of revolution; mean curvature; Gauss curvature.  

AMS Subject classification: Primary:  53A10  

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Acta Mathematica Universitatis Comenianae
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