• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.1-19
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• 2020

Using the complex parabolic rotations of holomorphic null curves in ℂ⁴ we transform minimal surfaces in Euclidean space ℝ³ to a family of degenerate minimal surfaces in Euclidean space ℝ⁴. Applying our deformation to holomorphic null curves in ℂ³ induced by helicoids in ℝ³, we discover new minimal surfaces in ℝ⁴ foliated by hyperbolas or straight lines. Applying our deformation to holomorphic null curves in ℂ³ induced by catenoids in ℝ³, we rediscover the Hoffman-Osserman catenoids in ℝ⁴ foliated by ellipses or circles.