Constant angle surfaces in ℍ2 × ℝ

Article

Abstract

We classify all surfaces in ℍ2 × ℝ for which the unit normal makes a constant angle with the ℝ-direction. Here ℍ2 is the hyperbolic plane.

Keywords

surfaces product manifold 

Mathematical subject classification

53B25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Cermelli and A.J. Di Scala. Constant-angle surfaces in liquid crystals. Philosophical Magazine, 87(12) (2007), 1871–1888.CrossRefGoogle Scholar
  2. [2]
    F. Dillen, J. Fastenakels, J. Van der Veken and L. Vrancken. Constant Angle Surfaces in S 2 × ℝ. Monaths. Math., 152(2) (2007), 89–96.MATHCrossRefGoogle Scholar
  3. [3]
    F. Dillen and M.I. Munteanu. Surfaces in ℍ 2 × ℝ. Pure and Applied Differential Geometry, PADGE 2007, Berichte aus der Mathematik (Shaker Verlag) Eds. Franki Dillen, Ignace Van de Woestyne, 185–193.Google Scholar
  4. [4]
    J. Fastenakels, M.I. Munteanu and J. Van der Veken. Constant angle surfaces in the Heisenberg group, preprint.Google Scholar
  5. [5]
    M.I. Munteanu and A.I. Nistor. A new approach on constant angle surface in E 3, to appear in Turkish J. Math., (2009).Google Scholar
  6. [6]
    P. Petersen. Riemannian Geometry. Graduate Texts in Mathematics, Springer Verlag, (1997).Google Scholar
  7. [7]
    J.G. Ratcliffe. Foundations of Hyperbolic Manifolds. 2-nd Edition, Graduate Texts in Mathematics, Springer (2006).Google Scholar

Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.Departement WiskundeKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Faculty of MathematicsUniversity ‘Al.I.Cuza’ of IaşiIaşiRomania

Personalised recommendations