Dimitrios E. Kalikakis, "A characterization of regular saddle surfaces in the hyperbolic and spherical three-space", Abstract and Applied Analysis, vol. 7, Article ID 764935, 7 pages, 2002. https://doi.org/10.1155/S1085337502203036
A characterization of regular saddle surfaces in the hyperbolic and spherical three-space
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.
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