Infinitesimal transformations of a symmetric Riemannian space of the first class

Анотація

The study of infinitesimal transformations in Riemannian spaces is of interest both theoretically and as an application. If a certain field is specified in the space $V_n$ with the metric $d{s}^2$, which admits an $r$-parametric group of motions $G_r$, then this field has $r$ conservation laws. The distribution of relativistic gas according to the Maxwell-Boltzmann law is characterized by a vector ${\xi }^i\left(x\right)$, which is a Killing vector (if the gas consists of particles of nonzero rest mass) or an infinitely small conformal transformation vector (if the gas consists of particles of zero rest mass). ([5],[6]) In this article, infinitesimal motions in symmetric Riemannian spaces of the first class $V_n$ were studied. For $n=4$ the basis of the Lie group $G_8$ of examined transformations is explicitly found and the structure of this group is given.