论文标题
在p-biharmonic曲线上
On p-biharmonic curves
论文作者
论文摘要
在本文中，我们将$ p $ -biharmonic曲线研究为Biharmonic曲线的自然概括。与Biharmonic曲线相反，如果$ p = \ frac {1} {2} $，则不需要具有恒定的地质曲率，而在这种情况下，它们的方程将其方程式减少到$ \ frac {1} {2} {2} $ - 弹性曲线。我们将对$ \ frac {1} {2} $ - 封闭表面上的Biharmonic曲线和三维空间表单，利用从文献中获得的$ \ frac {1} {2} $弹性曲线获得的结果。通过与磁性测量线建立连接，我们可以证明存在$ \ frac {1} {2} $ - Biharmonic曲线在封闭表面上。此外，我们将讨论$ p $ -Biharmonic曲线的稳定性。我们的分析强调了$ p $ -biharmonic和$ p $弹性曲线之间的一些有趣的关系。
In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their equation reduces to the one of $\frac{1}{2}$-elastic curves. We will classify $\frac{1}{2}$-biharmonic curves on closed surfaces and three-dimensional space forms making use of the results obtained for $\frac{1}{2}$-elastic curves from the literature. By making a connection to magnetic geodesic we are able to prove the existence of $\frac{1}{2}$-biharmonic curves on closed surfaces. In addition, we will discuss the stability of $p$-biharmonic curves with respect to normal variations. Our analysis highlights some interesting relations between $p$-biharmonic and $p$-elastic curves.
