Lie 代数胚与 Cartan 等价方法
微分几何
2012-03-07 v4 辛几何
摘要
Elie Cartan 的一般等价问题被重新表述于 Lie 代数胚的语言中。所得的形式体系无坐标且独立于模型，允许通过约化与扩充对 Cartan 等价方法进行完整的几何解释。我们展示了如何为有限型对象构造某些正规形（Cartan 代数胚），并能够将其直接解释为被曲率变形的无穷小对称性。细节针对传递结构展开，但该理论的基本原理包含非传递结构（非传递对称性变形）。详细的示例包括次黎曼接触结构与共形几何。
引用
@article{arxiv.math/0509071,
title = {Lie algebroids and Cartan's method of equivalence},
author = {Anthony D. Blaom},
journal= {arXiv preprint arXiv:math/0509071},
year = {2012}
}
备注
Version 4 (64 pages): The two introductory sections have been completely rewritten. This includes an explicit reformulation of the equivalence problem and improved paper outline. Added examples of almost complex structures and conformal parallelism. Abstract rewritten