Complete surfaces of constant curvature in H2 xR and S2 xR
2007 - J.A. Aledo, J.A. Gálvez, J.M. Espinar
Calculus of Variations and Partial Differential Equations 29, 347-363 (2007).
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces and . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature c > 0 into and a unique one into when c > 1, up to isometries of the ambient space. Moreover, we show that the hyperbolic plane of constant curvature c < −1 cannot be isometrically immersed into or .