Lie Algebras of Projective Motions of Five-Dimensional H-Spaces H<inf>221</inf> of Type {221}

Abstract

We study five-dimensional pseudo-Riemannian h-spaces $H_{221}$ of type $\{221\}$.Necessary and sufficient conditions are determined under which $H_{221}$ is aspace of constant (zero) curvature.Nonhomothetical projective motions in $H_{221}$ of nonconstant curvatureare found, homotheties and isometries of the indicated spaces are investigated.Dimensions, basis elements, and structure equations of maximal projective Liealgebras acting in $H_{221}$ of nonconstant curvature are determined.As a result, the classification of h-spaces $H_{221}$ of type $\{221\}$ by(non-homothetical) Lie algebras of infinitesimalprojective and affine transformations is obtained.