JournalsrmiVol. 30, No. 1pp. 309–316

Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded

  • Francisco Martín

    Universidad de Granada, Spain
  • Masaaki Umehara

    Tokyo Institute of Technology, Japan
  • Kotaro Yamada

    Tokyo Institute of Technology, Japan
Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded cover
Download PDF

Abstract

We construct a weakly complete flat surface in hyperbolic 3-space H3H^3 having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disk in the ideal boundary of H3H^3. This construction is accomplished as an application of minimal surface theory. This is an interesting phenomenon when one compares it with the fact that there are no complete non-flat minimal (resp. non-horospherical constant mean curvature one) surfaces in R3\mathbb{R}^3 (resp. H3H^3) having bounded Gauss maps (resp. bounded hyperbolic Gauss maps).

Cite this article

Francisco Martín, Masaaki Umehara, Kotaro Yamada, Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 309–316

DOI 10.4171/RMI/779