On Laguerre transformations in three-dimensional pseudo-Euclidean space and their analogs in the ideal area of Lobachevskii space

In the present paper we construct a 10-dimensional group which induces the Laguerre transformations of planes in the three-dimensional pseudo- Euclidean space ${}^1E_3$, and find action of this group on the tangent bundle of complex projective line, on the 4-dimensional pseudo-Euclidean space, and on the manifold of horospheres of the ideal area of three-dimensional Lobachevskii space.