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Archiv der Mathematik

, Volume 68, Issue 6, pp 520–528 | Cite as

Pseudo-spherical and pseudo-hyperbolic submanifolds via the quadric representation, I

  • Angel Ferrández
  • Pascual Lucas
  • Miguel Angel Meroño

Abstract.

We consider the quadric representation of a submanifold into non flat pseudo-Riemannian space forms. Then we classify submanifolds such that the mean curvature vector field of its quadric representation is proper for the Laplacian. We have got a complete characterization of hypersurfaces whose quadric representation satisfies \( {\it \tilde \Delta} {\tilde H} = {\it\lambda} {\tilde H} + {\it\mu} (\varphi -\varphi _0) \). As for surfaces into De Sitter and anti De Sitter worlds we have also found nice characterizations for minimal B-scrolls and complex circles.

Keywords

Vector Field Space Form Complete Characterization Curvature Vector Quadric Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • Angel Ferrández
    • 1
  • Pascual Lucas
    • 1
  • Miguel Angel Meroño
    • 1
  1. 1.Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, SpainES

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