Surfaces of Negative Curvature

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.KeywordsNegative CurvatureExtrinsic CurvatureIsometric ImmersionIntrinsic CurvatureSpherical ImageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.