Geodesic
Toward a Theory of Spaces of Constant Curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 42-54

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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. 
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     author = {V. S. Dryuma},
     title = {Toward a {Theory} of {Spaces} of {Constant} {Curvature}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a3/}
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V. S. Dryuma. Toward a Theory of Spaces of Constant Curvature. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 42-54. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a3/