微分几何，帕拉蒂尼引力和约化
Differential geometry, Palatini gravity and reduction
摘要：
本文讨论作为一般变分原理的所谓（真空）Palatini引力的一种表述。为了实现该目标，使用与框架束$LM$的连接束的几何形状相关的一些几何工具。拉格朗日-庞加莱约化方案的推广，这些类型的变分问题，使我们能够将其与爱因斯坦-希尔伯特变分问题。文中还讨论了它与文献中其它引力变分问题的关系。
英文摘要：
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle $LM$ are used. A generalization of Lagrange-Poincaré reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.
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。
