The scientific heritage of I. P. Egorov (July 25, 1915 -- October 2, 1990)
The article under review describes the scientific heritage of I. P. Egorov (July 25, 1915 -- October 2, 1990). The principal object of Egorov's research was the theory of lacunas in motion group orders and the geometries of their corresponding lacunary spaces. Starting with the Fubini theorem stating that there are no Riemannian spaces of dimension \(n\) with a complete isometry group \(G_r\) of order \(r=n(n+1)-1\) Egorov obtained his famous result that there exists no affine connection space admitting complete isometry group \(G_r\) of orders \(n^2< r<n^2+n\), finding an interval of ``forbidden'' isometry group orders named lacuna. Later Egorov determined the exact boundaries of some lacunas and characterized the spaces of the corresponding lacunarities. The article under review gives a complete account of these researches and corresponding methods based on Egorov's study of isometry equation integrability conditions as well as some other Egorov's results.
scientific article; zbMATH DE number 877640
scientific article