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SO(2)-invariant minimal and constant mean curvature surfaces. (English) Zbl 0827.53009

The authors endow \(\mathbb{R}^3\) with a certain classical 2-parameter family of homogeneous metrics whose isometry groups have dimension or 6, and then examine invariant constant mean curvature surfaces in these. Then description is made via an ODE which admits a prime integral.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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References:

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