Abstract
Our aim in the present article is to introduce and study new types of foldings of Lobachevsky space. Types of the deformation retracts of Lobachevsky space are presented. The relations between the foldings and the deformation retract of Lobachevsky spaces are deduced. Types of minimal retractions of Lobachevsky space are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retract after and before folding have been obtained. New types of homotopy maps are deduced.