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<p>Several methods to decompose a zero mean curvature surface in a certain space form into zero mean curvature surfaces in other space forms are known. For example, any non-planar minimal surface in Euclidean 3-space or maximal surface in Lorentz-Minkowski 3-space can be decomposed into a pair of zero mean curvature surfaces in isotropic 3-space. In this paper, we investigate the geometric properties that are preserved under such decompositions. To do this, we first show using Weierstrass representations that the decompositions under examination are unique. Then, we examine the planar curvature line condition, isometric deformation, and affine minimality of zero mean curvature surfaces, and show that these geometric properties are all preserved under the decompositions.</p>

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Geometric properties invariant under the decomposition of zero mean curvature surfaces

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Shintaro Akamine,
  • Joseph Cho,
  • Masaya Hara,
  • Yuta Ogata

摘要

Several methods to decompose a zero mean curvature surface in a certain space form into zero mean curvature surfaces in other space forms are known. For example, any non-planar minimal surface in Euclidean 3-space or maximal surface in Lorentz-Minkowski 3-space can be decomposed into a pair of zero mean curvature surfaces in isotropic 3-space. In this paper, we investigate the geometric properties that are preserved under such decompositions. To do this, we first show using Weierstrass representations that the decompositions under examination are unique. Then, we examine the planar curvature line condition, isometric deformation, and affine minimality of zero mean curvature surfaces, and show that these geometric properties are all preserved under the decompositions.