Abstract.
We obtain optimal height estimates for surfaces in ℍ2 × ℝ and \( \mathbb{S}^{2} \) × ℝ with constant Gaussian curvature K(I) and positive extrinsic curvature, characterizing the extreme cases as the revolution ones. Moreover, we get a representation for surfaces with constant Gaussian curvature in such ambient spaces, paying special attention to the cases of K(I) = 1 in \( \mathbb{S}^{2} \) × ℝ and K(I) = −1 in ℍ2 × ℝ.
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The first author is partially supported by Junta de Comunidades de Castilla-La Mancha, Grant No. PAI-05-034. The authors are partially supported by MEC-FEDER, Grant No. MTM2007-65249.
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Aledo, J.A., Espinar, J.M. & Gálvez, J.A. Surfaces with constant curvature in S2×R and H2×R. Height estimates and representation. Bull Braz Math Soc, New Series 38, 533–554 (2007). https://doi.org/10.1007/s00574-007-0059-9
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DOI: https://doi.org/10.1007/s00574-007-0059-9