Abstract and Applied Analysis
Volume 7 (2002), Issue 7, Pages 349-355
A characterization of regular saddle surfaces in the hyperbolic
and spherical three-space
Department of Mathematics, University of Crete Heraklion, Crete 714-09, Greece
Received 7 March 2002
Copyright © 2002 Dimitrios E. Kalikakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that the class of regular saddle surfaces in the
hyperbolic or spherical three-space coincides with the class of regular surfaces with
curvature not greater than the curvature of the surrounding space.
We also show that a similar result for nonregular surfaces is