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

Dimitrios E. Kalikakis

Abstract and Applied Analysis, 2002, vol. 7, 1-11

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 𝔼 3 .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:382157

DOI: 10.1155/S1085337502000799

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