标题： 关于不变仿射联络的度量性 显示英文标题

标题： On Metrizability of Invariant Affine Connections

摘要： 对于流形上相对于微分同胚群G不变的对称仿射联络的度量性问题进行了研究。 我们说该联络是G-度量的，如果它可表示为G-不变度量场的Levi-Civita联络。 在本文中，我们分析了旋转群G = SO(3)的G-度量性方程，该群在三维和四维欧几里得空间上以标准方式作用。 我们表明，联络具有SO(3)-不变性这一性质使我们能够找到所有SO(3)-度量性方程解的完整显式描述。 显示英文摘要

摘要： The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection of a G-invariant metric field. In this paper we analyze the G-metrizability equations for the rotation group G = SO(3), acting canonically on three- and four-dimensional Euclidean spaces. We show that the property of the connection to be SO(3)-invariant allows us to find complete explicit description of all solutions of the SO(3)-metrizability equations.