论文标题
三维同质空间中的三臂曲线
Triharmonic Curves in 3-Dimensional Homogeneous Spaces
论文作者
论文摘要
我们首先证明，与Biharmonic情况不同，在合适的riemannian歧管中，存在具有非稳定曲率的三摩尼克曲线。然后，我们对具有恒定高斯曲率的表面中的三臂曲线进行完整分类。接下来，限制了在三维的riemannian歧管中曲线的曲线，我们研究了具有持续曲率的三臂曲线曲线家族，表明它们是Frenet螺旋。在最后一部分中，我们在空间形式和bianchi-cartan-vranceanu空间中全面分类了三臂Frenet螺旋。
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces with constant Gaussian curvature. Next, restricting to curves in a 3-dimensional Riemannian manifold, we study the family of triharmonic curves with constant curvature, showing that they are Frenet helices. In the last part, we give the full classification of triharmonic Frenet helices in space forms and in Bianchi-Cartan-Vranceanu spaces.
