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TITLE UNIQUENESS OF FAMILIES OF MINIMAL SURFACES IN R-3
KIAS AUTHORS Lee, Eunjoo
JOURNAL JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2018
ARCHIVE  
ABSTRACT We show that an umbilic-free minimal surface in R-3 belongs to the associate family of the catenoid if and only if the geodesic curvatures of its lines of curvature have a constant ratio. As a corollary, the helicoid is shown to be the unique umbilic-free minimal surface whose lines of curvature have the same geodesic curvature. A similar characterization of the deformation family of minimal surfaces with planar lines of curvature is also given.
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