接触系与corank 1对合子分布
Contact systems and corank one involutive subdistributions
摘要：
本文给出了一个分布（或一个Pfidian系统）局部等价于J_n（R，R_m）（R到R_m的映射的n-喷注空间）上的正则接触系统的充要几何条件。我们研究这类系统的几何，特别是corank 1对合子分布的存在性。我们还区分了正则点和奇点，在正则点处，系统等价于正则接触系统，在奇点处，我们提出了一种新的规范形，它以类似于Kumpera-Ruiz规范形推广Jn（R，R）上的正则接触系统的方式推广了Jn（R，R）上的正则接触系统，也称为Goursat规范形。
英文摘要：
We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistributions. We also distinguish regular points, at which the system is equivalent to the canonical contact system, and singular points, at which we propose a new normal form that generalizes the canonical contact system on Jn(R,Rm) in a way analogous to that how Kumpera-Ruiz normal form generalizes the canonical contact system on Jn(R,R), which is also called Goursat normal form.
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