AI 中文总结
该研究针对从常微分方程经典范构造得到的锥结构，证明以n维射影空间一般曲线或3维射影空间直纹曲面为模型的平凡锥结构是平坦的，并探讨了其在相关领域的应用。
AI 中文摘要
可微流形上的锥结构是切丛中的锥场。若锥结构在每一点的射影化锥都与射影空间中某固定浸入子流形射影等价，则称该锥结构是平凡的，以该子流形为模型。我们考虑通过典范构造从常微分方程得到的锥结构，证明该类中以n维射影空间中的一般曲线或3维射影空间中的直纹曲面为模型的平凡锥结构是平坦的，还讨论了其在4维因果几何及无散Lax系统中的应用。
英文摘要
Cone structures on differentiable manifolds are fields of cones in the tangent bundle. A cone structure is isotrivial, modeled on a fixed immersed submanifold of the projective space, if at each point the projectivised cone is projectively equivalent to that submanifold. We consider cone structures arising from ordinary differential equations via a canonical construction. We prove that isotrivial cone structures in this class, modeled on generic curves in the $n$-dimensional projective space or ruled surfaces in the three-dimensional projective space, are flat. We also discuss applications to causal geometries in four dimensions and dispersionless Lax systems.
