TITLE

# Complete surfaces of constant curvature in H2 ï¿½ R and S2 ï¿½ R

AUTHOR(S)
Aledo, Juan; Espinar, Jos�; G�lvez, Jos�
PUB. DATE
July 2007
SOURCE
Calculus of Variations & Partial Differential Equations;Jul2007, Vol. 29 Issue 3, p347
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces $${\mathbb{H}^2\times\mathbb{R}}$$ and $${\mathbb{S}^2\times\mathbb{R}}$$ . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature c > 0 into $${\mathbb{H}^2\times\mathbb{R}}$$ and a unique one into $${\mathbb{S}^2\times\mathbb{R}}$$ 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 $${\mathbb{H}^2\times\mathbb{R}}$$ or $${\mathbb{S}^2\times\mathbb{R}}$$ .
ACCESSION #
24941142

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