Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions

Abstract

The article gives a classification of metrics of specialized Riemannian spaces, which carry four algebras at once in metrics Dm1 – real numbers, Cm2 – complex numbers, Hm3 – quaternions, Om4 – octions. Dimension of spaces n=m1+2m2+4m3+8m4 .The article presents a picture of lacunar spaces Vn4a also a classification of metrics by groups of isometric Gr and homothetic Pr movements (r is the dimension of the group) is given. There are gaps in the orders r of these groups, which are called lacunae. Here are two lacunae and metrics of spaces Vn4a of the first three lacunarities in the image of I. P. Egorov. It is established that among the orders of r-groups of isometries Gr and homoteties Pr in specialized Riemann spaces Vn4a of the third lacunarity, there is one order r3max – 1, which is not feasible e. g. a punctate lacunarity was found.

Keywords

• isometrie
• homotetie
• groups of isometries and homoteties
• order of groups
• lacunae
• spaces of <i>k</i>-th lacunarity