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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.

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