Mergulhos isométricos do plano hiperbólico em espaços Euclidianos - Vieira, Wilian Eurípedes (2009)
In this dissertation we present analytic expressions for isometric embeddings of hyperbolic plane (H2; ds) with Riemannian metric ds2 = dx2 + cosh2 (x) dy2 in Euclidean spaces R6 and S8 ½ R9. Besides isometric embeddings, we present analytic expressions for isometries between the Euclidean models of the Poincaré disk, Upper Half-Plane and the model (H; ds) cited above, for the Plane Hyperbolic Geometry. In this way, it is possible isometrically embed point lattices of hyperbolic plane in Euclidean environments, what can be useful for Coding and Information Theory.