突变理论中曲率的一般概念
General Notion of Curvature in Catastrophe Theory Terms
摘要：
我们引入了一个新的概念的曲率的超连接，不同的一个获得了一个纯粹的代数类比的曲率的线性连接。这个关于超连通曲率的新概念的自然性来自于对向量丛光滑截面奇点的研究（突变理论）。我们证明，经典的例子障碍的局部等价：外微分2-形式，黎曼张量，韦尔张量，曲率的线性连接和Nijenhuis张量可以处理的一个一般的方法。这种方法，适用于超连接导致一个新的概念的曲率（本文提出）的超连接。
英文摘要：
We introduce a new notion of a curvature of a superconnection, different from the one obtained by a purely algebraic analogy with the curvature of a linear connection. The naturalness of this new notion of a curvature of a superconnection comes from the study of singularities of smooth sections of vector bundles (Catastrophe Theory). We demonstrate that the classical examples of obstructions to a local equivalence: exterior differential for 2-forms, Riemannian tensor, Weil tensor, curvature of a linear connection and Nijenhuis tensor can be treated in terms of one general approach. This approach, applied to the superconnection leads to a new notion of a curvature (proposed in this paper) of a superconnection.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
