Web geometry of a system of n first order autonomous ordinary differential equations

Paraconformal structures, ordinary differential equations and totally geodesic manifolds

We construct point invariants of ordinary differential equations that generalise the Cartan invariants of equations of order two and three. The vanishing of the invariants is equivalent to the existence of a totally geodesic paraconformal structure which consist of a paraconformal structure, an adapted $GL(2,\R)$-connection and a two-parameter family of totally geodesic hypersurfaces on the solution space. The structures coincide with the projective structures in dimension 2 and with the Einstein-Weyl structures of Lorentzian signature in dimension 3. We show that the totally geodesic paraconf…

常微分与校准微分算子：在曲线网中的应用

Ordinary and calibrated differential operators Application to curvilinear webs

本文研究线性齐次微分算子定义的偏微分方程解空间维数，提出常微分与校准算子的概念，构造带重言联络的向量丛并以曲率刻画维数障碍，应用于曲线网重新得到 Damiano 上界并推广曲率定义。