This article is cited in 3 papers

Toward a Theory of Spaces of Constant Curvature

V. S. Dryuma

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: We construct some examples of three-dimensional metrics of constant curvature defined by the solutions of nonlinear integrable differential equations and their generalizations and study the properties of Riemann extensions of the metrics of constant curvature. We discuss the connection with the theory of normal Riemannian spaces.

Keywords: Riemann extension, spaces of constant curvature, Korteveg-de Vries equation.

DOI: 10.4213/tmf2007

 English version: Theoretical and Mathematical Physics, 2006, 146:1, 34–44

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