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2 results

  • PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ2×ℝ

  • Part of
  • RICARDO SA EARP
  • Journal:
    Journal of the Australian Mathematical Society / Volume 85 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 113-143
    Print publication:
    August 2008
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  • In thispaper we find many families in the product space ℍ2×ℝ of complete embedded, simply connected, minimal and surfaces with constant mean curvature H such that |H|≤1/2. We study complete surfaces invariant either by parabolic or by hyperbolic screw motions. We study the notion of isometric associate immersions. We exhibit an explicit formula for a Scherk-type minimal surface. We give a one-parameter family of entire vertical graphs of mean curvature 1/2. We prove a generalized Bour lemma that can be applied to ℍ2×ℝ,𝕊2×ℝ and to Heisenberg’s space to produce a family of screw motion surfaces isometric to a given one.

  • Invariant submanifolds in flow geometry

  • Part of
  • J. C. González-Dávila, M. C. González-Dávila, L. Vanhecke
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 62 / Issue 3 / June 1997
    Published online by Cambridge University Press:
    09 April 2009, pp. 290-314
    Print publication:
    June 1997
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  • We begin a study of invariant isometric immersions into Riemannian manifolds (M, g) equipped with a Riemannian flow generated by a unit Killing vector field ξ. We focus our attention on those (M, g) where ξ is complete and such that the reflections with respect to the flow lines are global isometries (that is, (M, g) is a Killing-transversally symmetric space) and on the subclass of normal flow space forms. General results are derived and several examples are provided.