Abstract
In the present paper, we first formulate and classify complete rotational surfaces with constant Gaussian curvature in the product spaces Q ε 2 × S1, where Q ε 2 denotes either the unit sphere S2 (when ε = 1) or the hyperbolic plane H2 of constant curvature −1 (when ε = −1). On the basis of this, we establish existence and uniqueness theorems for more general complete surfaces immersed in either S2 × S1 or in H2 × S1. As the result, we established a classification for these surfaces in Q ε 2 × S1 with a given constant K as the Gaussian curvature.
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Research supported by grants of NSFC (No. 11171091 and No. 11371018).
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Li, X., Qi, M. Complete surfaces in the product spaces Q ε 2 × S1 with constant Gaussian curvature. Bull Braz Math Soc, New Series 47, 1007–1035 (2016). https://doi.org/10.1007/s00574-016-0201-7
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DOI: https://doi.org/10.1007/s00574-016-0201-7