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<p>The focus is on circular nets with one or two families of spherical parameter lines, which are treated in Möbius geometry. These circular nets provide a discretisation of surfaces with one or two families of spherical curvature lines. The special cases of planar, circular and linear parameter lines are also investigated. A Lie-geometric discretisation in terms of principal contact element nets is also presented. Its properties are analogous to the classical properties of surfaces with one or two families of spherical curvature lines. Circular nets with two families of spherical parameter lines have geometric properties that are related to Darboux cyclides. Circular nets with one or two families of spherical parameter lines are examples of Q-nets with terminating Laplace sequences. More generally, this article considers Q-nets that are inscribed in quadrics and that have terminating Laplace sequences.</p>

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Circular Nets with Spherical Parameter Lines and Terminating Laplace Sequences

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月25日

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  • Alexander I. Bobenko,
  • Alexander Y. Fairley

摘要

The focus is on circular nets with one or two families of spherical parameter lines, which are treated in Möbius geometry. These circular nets provide a discretisation of surfaces with one or two families of spherical curvature lines. The special cases of planar, circular and linear parameter lines are also investigated. A Lie-geometric discretisation in terms of principal contact element nets is also presented. Its properties are analogous to the classical properties of surfaces with one or two families of spherical curvature lines. Circular nets with two families of spherical parameter lines have geometric properties that are related to Darboux cyclides. Circular nets with one or two families of spherical parameter lines are examples of Q-nets with terminating Laplace sequences. More generally, this article considers Q-nets that are inscribed in quadrics and that have terminating Laplace sequences.