Surfaces with constant curvature in S2xR and H2xR. Height Estimates and Representation.
2007 - J.A. Aledo, J.A. Gálvez, J.M. Espinar
Bulletin of the Brazilian Mathematical Society 38, 533-554 (2007).
We obtain optimal height estimates for surfaces in ℍ2 × ℝ and × ℝ with constant Gaussian curvature K(I) and positive extrinsic curvature, characterizing the extreme cases as the revolution ones. Moreover, we get a representation for surfaces with constant Gaussian curvature in such ambient spaces, paying special attention to the cases of K(I) = 1 in × ℝ and K(I) = −1 in ℍ2 × ℝ.