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
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 , which is bounded by a rectifiable curve, is a
space of curvature not greater than in the sense of
Aleksandrov. This generalizes a classical theorem by Shefel' on
saddle surfaces in .