Complete surfaces of constant curvature in H2 × R and S2 × R

By J. Aledo, J. Espinar, J. A. Gálvez. 2005

55 citations recorded by the source corpus.

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 $${\mathbb{S}^2\times\mathbb{R}}$$ .

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/79fc485b65a986f1a36d7651d582d5c9d233d233

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Totally umbilic surfaces in homogeneous 3-manifolds (2006, unknown): “See for example [14], [6], [7], [17], [15], [12], [13], [11], [9], [4], [2], [10], [5] and [8].”
Complete surfaces with positive extrinsic curvature in product spaces (2007, background): “Aledo, Espinar and Gálvez associated a holomorphic quadratic differential to constant Gaussian curvature surfaces in S(2) R and H(2) R, [AEG1].”