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Deformation of minimal surfaces with planar curvature lines. (English) Zbl 1381.53023
Minimal surfaces with planar curvature lines constitute a classical topic of differential geometry. In this paper, the authors re-visit this topic, giving parameterizations of all such surfaces. From these parameterizations, they prove the existence of axial directions and show that there exists a continuous deformation between all these surfaces. As a by-product, they characterize those minimal surfaces which are also affine minimal surfaces as the conjugate of minimal surfaces with planar curvature lines.

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53A15 Affine differential geometry
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