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On the Gauss map of B-scrolls in 3-dimensional Lorentzian space forms
Authors:Angel Ferrández  Pascual Lucas
Affiliation:(1) Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain;(2) Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
Abstract:In this note we show that B-scrolls over null curves in a 3-dimensional Lorentzian space form 
$$overline M _1^3 left( c right)$$
are characterized as the only ruled surfaces with null rulings whose Gauss maps G satisfy the condition 
$$Delta G = Lambda G,Lambda :xleft( {overline M } right)$$
being a parallel endomorphism of 
$$xleft( {overline M } right)$$
.
Keywords:Gauss map  B-scroll  ruled surfce
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