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Geometry III pp 87-178 | Cite as

Surfaces of Negative Curvature

Chapter
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 48)

Abstract

This article is devoted to surfaces of negative Gaussian curvature K < 0 in three-dimensional Euclidean space E 3 and related problems. These surfaces constitute part of the class of saddle surfaces in E N . Hence the article serves as an extension of the third chapter of Part I of this book, written by Yu.D. Burago and S.Z. Shefel’. At the same time, this article is meant to be read independently, and so together with the references to Alekseevskij, Vinogradov and Lychagin (1988), Alekseevskij, Vinberg and Solodovnikov (1988), Burago and Shefel’ (1989), and Sabitov (1989b), we repeat certain facts in the text that are already reflected in these surveys. However, these repetitions are comparatively small.

Keywords

Negative Curvature Extrinsic Curvature Isometric Immersion Intrinsic Curvature Spherical Image 
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