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Abstract and Applied Analysis
Volume 7, Issue 7, Pages 349-355
http://dx.doi.org/10.1155/S1085337502203036

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 Hindawi Publishing Corporation. 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.

Abstract

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 incorrect.