黎曼流形中运动群不变量

Invariant of Group of Motions in Riemann Manifold

黎曼流形运动群的研究是微分几何中一个重要问题。本文构造了黎曼流形中亏数为 2的一个运动群 ,进而对黎曼流形度规运动群、共形运动群以及亏数为 2的运动群的黎曼不变量进行了刻划。文中证明上述三个运动群之间存在着某种所谓“自相关性”。此外 。

Research of the group of motions in Riemann manifold is an important question of the differential geometry. This paper stractures a group of motions about the defective number two in Riemann manifold. It portraies Riemann′s invariant in Riemann′s manifold about the group of motions of the gauge,conformal and defective number being two. The three groups of motions are proven to have the quality of self-correlation in them. This paper shows an interesting example that the conformal group of motions in Riemann space becomes the gauge group of motions in conformal space.