A characterization ofweingarten surfaces in hyperbolic 3-space

Nikos Georgiou, Brendan Guilfoyle

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We study 2-dimensional submanifolds of the space L(ℍ3) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. Such a surface is Lagrangian iff there exists a surface in ℍ3 orthogonal to the geodesics of σ We prove that the induced metric on a Lagrangian surface in L(ℍ3) has zero Gauss curvature iff the orthogonal surfaces in ℍ3 are Weingarten: the eigenvalues of the second fundamental form are functionally related.We then classify the totally null surfaces in L(ℍ3) and recover the well-known holomorphic constructions of flat and CMC 1 surfaces in H3.

Original languageEnglish
Pages (from-to)233-253
Number of pages21
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume80
Issue number2
DOIs
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Hyperbolic 3-space
  • Kähler structure
  • Weingarten surfaces

Fingerprint

Dive into the research topics of 'A characterization ofweingarten surfaces in hyperbolic 3-space'. Together they form a unique fingerprint.

Cite this