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A complete classification of parallel surfaces in three-dimensional homogeneous spaces. (English) Zbl 1136.53016

From the introduction: In the present paper, we complete the classification of parallel and totally geodesic surfaces in all three-dimensional homogeneous spaces by solving the problem in three-dimensional Lie groups with a left-invariant metric yielding a three-dimensional isometry group. To do this, we make a distinction between unimodular and non-unimodular groups.

MSC:

53B25 Local submanifolds
53C40 Global submanifolds
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