论文标题
所有类三阶odes的子曼叶的几何形状，作为riemannian歧管
Geometry of submanifolds of all classes of third-order ODEs as a Riemannian manifold
论文作者
论文摘要
在本文中，我们证明，与线性二阶ODE相对应的任何表面在所有类别的三阶ODES中，$ y''''= f（x，y，y，p，q）$作为riemannian歧管，$ y'= p $和$ y''''= q $，仅在$ q_ $ q_ yy} = 0 $ {yy} = 0 $} = 0 $。此外，我们将看到带有常规形式$ y'''''= \ pm y+β（x）$的线性二阶ode是唯一定义最小表面并且也完全是大地测量的情况。
In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs $y'''=f(x, y, p, q)$ as a Riemannian manifold where $y'=p$ and $y''=q$, if and only if $q_{yy}=0$. Moreover, we will see the linear second-order ODE with general form $y''=\pm y+β(x)$ is the only case that is defined a minimal surface and is also totally geodesic.
