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MINIMAL SURFACES IN ℝ4 FOLIATED BY CONIC SECTIONS AND PARABOLIC ROTATIONS OF HOLOMORPHIC NULL CURVES IN ℂ4

  • Lee, Hojoo (Department of Mathematics and Institute of Pure and Applied Mathematics Jeonbuk National University)
  • Received : 2018.05.29
  • Accepted : 2019.09.25
  • Published : 2019.12.30

Abstract

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.

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