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Complete surfaces of constant curvature in H2xR and S2xR

Juan A. Aledo·Jose M. Espinar·Jose A. Galvez
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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.

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Juan A. Aledo, Jose M. Espinar, Jose A. Galvez. 2005-10-15. Complete surfaces of constant curvature in H2xR and S2xR. https://arxiv.org/abs/math/0510321

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