The problem of realizing the Lobachevsky geometry in Euclidean space

Andrey Popov
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Andrey Popov: Lomonosov Moscow State University, Department of Mathematics

Chapter Chapter 2 in Lobachevsky Geometry and Modern Nonlinear Problems, 2014, pp 61-126 from Springer

Abstract: Abstract In this chapter we deal with general problems connected with the realization of the two-dimensional Lobachevsky geometry in the three-dimensional Euclidean space. In particular, we give an exposition of Lobachevsky planimetry as the geometry of a two-dimensional Riemannian manifold of constant negative curvature.We describe the apparatus of fundamental systems of equations of the theory of surfaces in $$\mathbb{E}^3$$ and discuss specifics of its application to the analysis of surfaces of constant negative Gaussian curvature.

Keywords: Euclidean Space; Fundamental Form; Radius Vector; Isometric Immersion; Geodesic Curvature (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-05669-2_3

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DOI: 10.1007/978-3-319-05669-2_3

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