A characterization of regular saddle surfaces in the hyperbolic and spherical three-space. (21st August 2002) - Kalikakis, Dimitrios E.
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.