$\mathbb{H}^2 \times \mathbb{R}$中的弧叶极小曲面族及其Jacobi域
Families of minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ foliated by arcs and their Jacobi fields
摘要：
本文对$\mathbb{H}^2 \times \mathbb{R}$中一个有趣的已知极小曲面族提供了一些新的观点和计算方法。在这个家庭中的表面是悬链面，抛物线悬链面和高矩形。每一个都由$\mathbb{H}^2$的水平拷贝中的圆形、水平圆或圆弧形成叶状。所有这些表面都是众所周知的，但这里的重点是它们的统一特征和它们位于一个连续的家族中的事实。我们还开始了研究的Jacobi算子的抛物线悬链线，并计算Jacobi领域的变形在这个家庭中的其他两种类型的表面。
英文摘要：
This note provides some new perspectives and calculations regarding an interesting known family of minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$. The surfaces in this family are the catenoids, parabolic catenoids and tall rectangles. Each is foliated by either circles, horocycles or circular arcs in horizontal copies of $\mathbb{H}^2$. All of these surfaces are well-known, but the emphasis here is on their unifying features and the fact that they lie in a single continuous family. We also initiate a study of the Jacobi operator on the parabolic catenoid, and compute the Jacobi fields associated to deformations to either of the two other types of surfaces in this family.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
