Premium
Complete surfaces in the hyperbolic space with a constant principal curvature
Author(s) -
Aledo Juan A.,
Gálvez José A.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310296
Subject(s) - mathematics , principal curvature , constant (computer programming) , hyperbolic space , statement (logic) , space (punctuation) , curvature , constant curvature , principal (computer security) , surface (topology) , mathematical analysis , space form , mean curvature , pure mathematics , geometry , law , linguistics , philosophy , submanifold , computer science , political science , programming language , operating system
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)