论文标题
双曲线空间中革命的capanies和最小表面
Catenaries and minimal surfaces of revolution in hyperbolic space
论文作者
论文摘要
我们介绍了双曲平面中外链链纤维的概念。从环境空间中可以看出，在倍曲底模型中工作，将外部链纳级定义为悬挂在其重量下的曲线的形状。换句话说，外部链纳级是电势功能的关键点，在该功能中，我们在环境洛伦兹空间中以外在距离与固定参考平面的外在距离计算电势。然后，我们根据其曲率表征外部链球菌，并将其作为解决涉及某些矢量场的规定曲率问题的解决方案。此外，我们证明双曲线空间中任何最小革命表面的生成曲线是相对于适当的参考平面的外部链式。最后，我们证明，如果我们用肉眼骨正交的内在长度代替了参考地测量的家族，则在外部链球菌的固有距离中可以接受内在的特征。
We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an extrinsic catenary is a critical point of the potential functional, where we calculate the potential with the extrinsic distance to a fixed reference plane in the ambient Lorentzian space. We then characterize extrinsic catenaries in terms of their curvature and as a solution to a prescribed curvature problem involving certain vector fields. In addition, we prove that the generating curve of any minimal surface of revolution in the hyperbolic space is an extrinsic catenary with respect to an appropriate reference plane. Finally, we prove that one of the families of extrinsic catenaries admits an intrinsic characterization if we replace the extrinsic distance with the intrinsic length of horocycles orthogonal to a reference geodesic.
