Foundations of Lobachevsky geometry: axiomatics, models, images in Euclidean space

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

Chapter Chapter 1 in Lobachevsky Geometry and Modern Nonlinear Problems, 2014, pp 15-59 from Springer

Abstract: Abstract This first chapter is devoted to an exposition of the foundations of Lobachevsky geometry, formed by three classical components: axiomatics, model interpretations, and investigation of surfaces of constant negative curvature. The discussion of these parts is carried out keeping in mind what is required for their application to problems of contemporary mathematical physics.

Keywords: Disc Model; Cross Ratio; Constant Negative Curvature; Classical Surface; Cuspidal Edge (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_2

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DOI: 10.1007/978-3-319-05669-2_2

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