Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 191208 (2004) 

On a conjecture about the Gauss map of complete spacelike surfaces with constant mean curvature in the LorentzMinkowski spaceRosa M. B. Chaves and Claudia Cueva C\^ andidoDepartamento de Matemática, Instituto de Matemática e Estatística, Universidade de S\ ao Paulo, Caixa Postal 66281, CEP 05315970, SP Brazil, email: rosab@ime.usp.br email: cueva@ime.usp.brAbstract: The Gauss map of complete helicoidal (consequently rotational) surfaces with nonzero constant mean curvature in the Euclidean 3space contains a maximal circle of the sphere. Observing the Gauss map image for complete spacelike surfaces in the LorentzMinkowski 3space ${\mathbb L}^3$, we propose the following conjecture: ``Given a complete spacelike surface in ${\mathbb L}^3$, with nonzero constant mean curvature, its Gauss map image contains an arbitrary maximal geodesic of the hyperboloid contained in ${\mathbb L}^3$''. We answer the conjecture for the special class of spacelike rotational surfaces in ${\mathbb L}^3$ and obtain that, in this case, the conjecture is also true, as in the Euclidean space ${\mathbb R}^3$. Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
