Abstract and Applied Analysis
Volume 7 (2002), Issue 7, Pages 349-355
doi:10.1155/S1085337502203036

A characterization of regular saddle surfaces in the hyperbolic and spherical three-space

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.