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Levi-Civita Connection

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2024年

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  • Ulrich Pinkall,
  • Oliver Gross

摘要

The Levi-Civita connection of a surface \(f\colon M \to \mathbb {R}^3\) provides a geometrically meaningful way to take directional derivatives of a vector field Y  on M. Based on the Levi-Civita connection we derive two important equations that are satisfied by the curvature of a surface in \(\mathbb {R}^3\) : the Gauss equation and the Codazzi equation.