Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 113-123

On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space

Dimitrios E. Kalikakis1,2

1Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana 61801, IL, USA
2Department of Applied Mathematics, University of Crete, Heraklion, Crete 714-09, Greece

Received 9 November 2001

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.


This paper proves that any nonregular nonparametric saddle surface in a three-dimensional space of nonzero constant curvature k, which is bounded by a rectifiable curve, is a space of curvature not greater than k in the sense of Aleksandrov. This generalizes a classical theorem by Shefel' on saddle surfaces in 𝔼3.