Complete surfaces in the product spaces Q ε 2 x S1 with constant Gaussian curvature

作者：Li, Xingxiao^*; Qi, Min

来源：Bulletin of the Brazilian Mathematical Society, 2016, 47(4): 1007-1035.

DOI：10.1007/s00574-016-0201-7

• complete surfaces
• constant Gaussian curvature
• classification theorem
• rotational surfaces

In the present paper, we first formulate and classify complete rotational surfaces with constant Gaussian curvature in the product spaces Q (epsilon) (2) x S-1, where Q (epsilon) (2) denotes either the unit sphere S-2 (when epsilon = 1) or the hyperbolic plane H-2 of constant curvature -1 (when epsilon = -1). On the basis of this, we establish existence and uniqueness theorems for more general complete surfaces immersed in either S-2 x S-1 or in H-2 x S-1. As the result, we established a classification for these surfaces in Q (epsilon) (2) x S-1 with a given constant K as the Gaussian curvature.

• 出版日期2016-12
• 单位河南师范大学