论文标题
机械师的广义和分级几何形状：全面介绍
Generalized and graded geometry for mechanics: a comprehensive introduction
论文作者
论文摘要
在本文中，我们概述了有关差异几何形状最近“发现”的结果，例如较高的结构和差异级别的流形，其中一些自然问题来自力学。我们解释说，可以使用Q结构的语言方便地描述许多在上下文中的经典差异几何构造，因此Q结构保存的集成器可能在机械方面极有用。我们提供了一些暗示，如何构建后者并提出一些开放问题。 由于该文本既打算用于数学和力学社区，因此我们也试图使非几何形状也可以使用。
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of classical differential geometric constructions in the context can be conveniently described using the language of Q-structures, and thus Q-structure preserving integrators are potentially of great use in mechanics. We give some hints how the latter can be constructed, and formulate some open problems. Since the text is intended both to mathematics and mechanics communities, we tried to make it accessible to non-geometers as well.
