Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded
Francisco Martín
Universidad de Granada, SpainMasaaki Umehara
Tokyo Institute of Technology, JapanKotaro Yamada
Tokyo Institute of Technology, Japan
Abstract
We construct a weakly complete flat surface in hyperbolic 3-space having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disk in the ideal boundary of . 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 (resp. ) 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