Abstract and Applied Analysis

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Abstract and Applied Analysis / 2002 / Article

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Volume 7 |Article ID 382157 | 11 pages | https://doi.org/10.1155/S1085337502000799

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, IL 61801, USA

2Department of Applied Mathematics, University of Crete, Heraklion, Crete 714-09, Greece

Received09 Nov 2001

Abstract

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.

Copyright © 2002 Hindawi Publishing Corporation. 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.

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