Isometric embeddings of the hyperbolic plane in Euclidean spaces / Mergulhos isométricos do plano hiperbólico em espaços Euclidianos
AUTOR(ES)
Wilian Eurípedes Vieira
DATA DE PUBLICAÇÃO
2009
RESUMO
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 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.
ASSUNTO(S)
isometria mergulho isométrico curvatura gaussiana isometria (matemática) isometric embedding plano hiperbólico matematica espaços hiperbólico isometry poincaré model gaussian curvature imersão isométrica modelo de poincaré geometria diferencial poincaré, séries de isometric imersion hyperbolic plane
