Complete surfaces in the hyperbolic space with a constant principal curvature

✍ Scribed by Juan A. Aledo; José A. Gálvez

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 110 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310296

✦ Synopsis

Abstract

In this paper we study complete orientable surfaces with a constant principal curvature R in the 3‐dimensional hyperbolic space H^3^. We prove that if R^2^ > 1, such a surface is totally umbilical or umbilically free and it can be described in terms of a complete regular curve in H^3^. When R^2^ ≤ 1, we show that this result is not true any more by means of several examples. This contradicts a previous statement by Zhisheng [6]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)