Complete surfaces of constant curvature in H2xR and S2xR
Differential Geometry
2007-05-23 v1
Abstract
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces H2xR and S2xR. In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature c>0 into H2xR and a unique one into S2xR 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 H2xR or S2xR.
Cite
@article{arxiv.math/0510321,
title = {Complete surfaces of constant curvature in H2xR and S2xR},
author = {Juan A. Aledo and Jose M. Espinar and Jose A. Galvez},
journal= {arXiv preprint arXiv:math/0510321},
year = {2007}
}
Comments
17 pages